There doesn’t appear to be much research on this topic, but here’s what the first source I found says (“SY” = Sefer Josippon):
The Christian-Arabic adaptation of the Hebrew SY makes its way to Ethiopia after the ascendancy of the so-called Solomonic dynasty in 1270. This political revolution spurs a renaissance of Ethiopic literature, which lasts well into the fifteenth century.175 In addition to the production of indigenous texts like the Kǝbrä Nägäśt, this time period also sees the revitalization of Ethiopian relations with Coptic Christians in Egypt. This change then provides an opportunity for the introduction of texts written in the surrounding areas to make their way into Ethiopia by way of translations. The Christian-Arabic adaptation of SY is one of the first of such texts to be translated and comes to be called the Zena Ayhud (or the History of the Jews), and represents an almost literal translation of the Arabic.176
The Solomonic Dynasty was the ruling dynasty of Ethiopia all the way until 1974, when they were overthrown by communists. They claimed to be descendants of Solomon and the Queen of Sheba, hence the name.
Although a precise date for the translation of the Zena Ayhud has remained elusive, almost all scholars agree that the text belongs to the large number of translations into Ethiopic that are made during the thirteenth and fourteenth centuries. As early as 1907, E. Littmann makes the case that the ZA is translated from the Arabic version of SY “in der Periode der Übersetzungsliteratur aus dem Arabischen (1270–ca. 1430).”180 Kamil agrees with Littman’s dating and sees no evidence to suggest another time period for the translation.181 More specifically, he posits that the ZA is most likely translated as part of the ecclesiastical reforms that take place with the ascendancy of Yekūnō Amlāk (1270–1285), who commissions the translation of large numbers of theological and ecclesiastical works into Ge’ez.182 Similarly, Witakowski places the translation at around the same time, namely c. 1300.183 While acknowledging that the text could have indeed been translated late in the thirteenth-century, Manfred Kropp suggests that the scribal cultures that flourish during the reign of Amdā Seyon (1314–1344) could have also served as the provenance of the translation.184
The thirteenth and fourteenth centuries see the resurgence and proliferation of monasticism in Ethiopia largely as the result of the military and political programs of two rulers: Yekūnō Amlāk and Amdā Seyon. In 1270, Yekūnō Amlāk puts an end to the Zagwē dynasty by killing the last Zagwē king and declares himself king, beginning what comes to be called the Solomonic Dynasty.191 In order to consolidate his newly-gained power, Yekūnō Amlāk allies himself with the Amhara and the Christian communities of the Shäwa region.His alliance with Christian communities is solidified by Amdā Seyon, who takes the throne in 1314. Amdā Seyon succeeds in conquering the most important Muslim strongholds in Ethiopia, including Īfat, which was considered the center of Muslim political power.192 He thus succeeds in not only consolidating the victories of Yekūnō Amlāk, but also in further extending the Christian territories beyond Shäwa and Amhara, to include northern territories such as Lasta and Tigrē.193
As part of their program to extend territories into non-Christian regions, the Christian rulers employ the influence of the royal court on the Ethiopian churches to evangelize non-Christians.194 In this effort, the royal patronage of monastic houses becomes an important tool of evangelization and Christian education. Tamrat notes, for example, that following his ascension to power, Yekūnō Amlāk makes a religious pact with Iyāsus-Mo’a, who founds one of the most important monastic houses in Ethiopia, Dabra Hayq.195 In addition to founding Dabra Hayq, Iyasus M’oa (d. 1292) also gains a number of students, who become important monks in their own right and found their own monasteries. A certain monk named Takla-Haymanot becomes the most famous of Iyasus M’oa’s students, himself founding several monastic houses (e.g Dabra Asbo, also known as Dabra Lībānōs). Takla-Haymanot becomes renowned for his conversion of many to Christianity, primarily through the education centers he establishes across the Christian territories.196
The theological and intellectual cultures of monastic houses such as Dabra Hayq and Dabra Asbo likely serve as the centers of the large number of translations from Arabic to Ge’ez 65 that are made during this time period. In addition to hagiographic literature, monastic rules, and theological writings, the translation of historiographical works from Arabic also becomes a part of the literary life of Ethiopian monasteries.197
Among the historiographical works listed below, the ZA stands out as a unique case because of its reception in the Ethiopian traditional as a biblical text.
In certain canon lists of the Ethiopian Orthodox Tewahedo Church, for example, the ZA appears as Maṣəhafa Yosēf Walda Koryon and is listed as the final book of the Old Testament.201 The reception of the Ethiopic version of SY as canonical largely stems from the fact that the text is already received by Coptic Christains as an important witness of the Maccabean tradition. The association made between the SY tradition and the books of Maccabees clearly makes its way into Ethiopia, as demonstrated in part by the fact that the ZA replaces the books of Maccabees in the canon list provided in the Fətḥa Nägäśt.202
If you don’t know about the Maccabees, in brief they were a family of Jews who rebelled against their Greek rulers and reestablished an independent Israel which lasted from “167 BCE to 37 BCE, being a fully independent kingdom from about 110 to 63 BCE”. In other words, they were the main figures in between the end of the Old Testament (which mostly stops in the 400s BC) and the start of the New Testament.
In conclusion, the monastic lives of medieval Ethiopian scholars most likely serves as the cultural and historical background for the translation of the Christian-Arabic version of SY into Ge’ez.The translation is made at a time when such scholars are becoming increasingly interested in both preserving Ethiopian history and anchoring Ethiopian history within the broader context of surrounding cultures. The ZA gains an important place among other historiographical works that are translated during this time period because it is seen as an important witness to a period in biblical history that is otherwise vacant in historical imagination of medieval Ethiopian monks. They understand the text as filling in the intertestamental gap, as well as further illuminating the historical context of the emergence of Christianity. They also view the text as canonical in nature, which affects the way in which the translation is made.
So according to this author, the work was accepted as canonical because it filled in a gap in history. Catholics and other Orthodox Christians fill in the gap with the Books of the Maccabees, which also cover this period, but perhaps the Ethiopians didn’t have access to those books, or they just chose to canonize a different work instead.
I assume this is somewhat different from how the other extra books in the Ethiopian canon got there, since most or all of the other books are much older.