It seems that the most acceptable view is that which places its composition at the end of the seventh or the beginning of the eighth century i.e. this jewish text post-dates quran !
The common theme appears to be that the stories of Solomon and Sheba as mentioned in the Targum Sheni are not to be seen in the rabbanic literature. The writer of the article in
Encyclopaedia Judaica points that:
Outstanding among the stories interwoven into the Targum Sheni is the variegated description of Solomon's throne (1:2)..... Some of these motifs are also found in the Koran (27:20-40), and it has been suggested that
the author [of Targum Sheni] also made use of Arabic sources.[19]
Similarly Edward Ullendorff says:
In the Jewish sources the combined narrative of Kur'an and Muslim commentators can first be traced in the 8th (?) century Targum Sheni to Esther where we find a most elaborate version of this story. This is further embellished in the 11th (?) century Alphabet of Ben Sira...[20]
The very "source" he had identified has been acknowledged by Western scholarship as redacted in its final form after the advent of Islam, and it is most likely that the Qur'an and its commentaries served as its sources. The revelation of the Qur'an arrived long before the final compilation of the Second Targum of Esther. And if it is argued that these Jewish sources may have existed in some form before redaction, and before the advent of Islam, then one has to prove the evidence. The manuscript evidence is certainly very hopeless. The earliest manuscript dates from 12th century CE, some 500 years after the advent of Islam . There are some Cairo Genizah fragments of Targum to Esther that contains unattested witnesses. If the Targum Sheni was so popular among the Jews why is there such a dearth of early manuscripts?
http://www.islamic-awareness.org/Quran/Sources/BBsheba.html
