I came across these:
[name_f]Bice[/name_f] (diminutive of [name_f]Beatrice[/name_f] in Italian–BtN lists the pronunciation as [name_f]BEE[/name_f]-che, which I think is a soft “E”, like “bet” or “send”)
[name_f]Cloe[/name_f]
[name_f]Febe[/name_f] (I don’t think it looks anywhere near as gorgeous as [name_f]Phoebe[/name_f], though)
[name_f]Ines[/name_f]
[name_u]Luce[/name_u] (LOO-cheh)
[name_f]Mimi[/name_f]
Those were the only ones I found on Behind the Name, although they had a lot of gorgeous ones that do end in “A”–[name_f]Vera[/name_f], [name_f]Sara[/name_f], Pina, [name_f]Lena[/name_f]/[name_f]Lina[/name_f], [name_f]Alma[/name_f], [name_f]Alba[/name_f], etc.–and that are longer–[name_f]Adelina[/name_f], [name_f]Alessandra[/name_f], [name_f]Antonia[/name_f], [name_f]Antonella[/name_f], [name_f]Amaranta[/name_f], [name_f]Annabella[/name_f], [name_f]Antonina[/name_f], [name_f]Arianna[/name_f], [name_f]Aurelia[/name_f], [name_f]Aurora[/name_f], [name_f]Benedetta[/name_f], [name_f]Bianca[/name_f], [name_f]Carolina[/name_f], [name_f]Caterina[/name_f], [name_f]Celestina[/name_f], [name_f]Celeste[/name_f] (cheh-LEST-eh, I think), [name_f]Cecilia[/name_f], [name_f]Clementina[/name_f], [name_f]Cosima[/name_f], [name_f]Dafne[/name_f] (och, this is one letter away from meeting her criteria!), [name_f]Delia[/name_f], [name_f]Elena[/name_f], [name_f]Eleonora[/name_f], [name_f]Leonora[/name_f], [name_f]Elisa[/name_f], [name_f]Eloisa[/name_f], [name_f]Emilia[/name_f], [name_f]Eugenia[/name_f], [name_f]Fiammetta[/name_f], Fioralba, [name_f]Fiorella[/name_f], [name_f]Gemma[/name_f], [name_f]Genoveffa[/name_f], [name_f]Ginevra[/name_f], [name_f]Giovanna[/name_f], [name_f]Isabella[/name_f], Loreto, [name_f]Maddalena[/name_f], [name_f]Mafalda[/name_f], [name_f]Mirabella[/name_f], [name_f]Mirella[/name_f], [name_f]Noemi[/name_f] (again, one letter off from fitting her criteria! I love [name_f]Noemi[/name_f]), [name_f]Ofelia[/name_f], [name_f]Ondina[/name_f], [name_f]Paolina[/name_f], [name_f]Rachele[/name_f] (rah-KELL-eh, I think? I could be wrong, though), [name_f]Rosella[/name_f], [name_f]Rosina[/name_f] ([name_u]LOVE[/name_u]!), [name_f]Simona[/name_f], [name_f]Sofia[/name_f], [name_f]Susanna[/name_f], [name_f]Tatiana[/name_f], [name_f]Valeria[/name_f], and [name_f]Zoe[/name_f] (again, only one letter off, but I don’t think most associate this with [name_f]Italy[/name_f]. I think more Greek, Turkish, [name_m]French[/name_m], or [name_m]German[/name_m] before Italian, but it is used internationally!).
Good luck to your friend!