According to an article in Wikipedia (https://it.wikipedia.org/wiki/Istituto_di_Studi_Superiori_di_Firenze), the institute was transformed into the Università degli Studi di Firenze in 1924. I suggest starting your search at their website (https://www.unifi.it/changelang-eng.html). There is a description of an oriental mss. collection here: https://www.sba.unifi.it/p1590.html.