Absolutely; there are thousands of compositions in A# Minor.
Firstly, there is no B minor chord in the key of F sharp minor. Rather, it is A sharp minor chord. And you can use any chord at the end of a chord progression. Why not!
D sharp minor
The parallel minor of F-sharp major is F-sharp minor. A parallel minor key is the one with the same tonic note.
There are no flats in b-minor. B major has two flats, both B-flat and A-flat, but b-flat minor is the relative minor of D-major, which has a sharp key signature. The sharps in b-minor are F-sharp and C-sharp.
Fx (f double sharp) minor.
The natural minor has 5 and the harmonic minor has 4 and a double sharp.
Four key signatures have G sharp and E sharp in them: F sharp Major, D sharp minor, C sharp Major and A sharp minor.
B Major and G sharp minor. The sharps are F, C, G, D, and A sharp, in that order.
E sharp minor
what is the relative minor of f sharp major
Toccata and fugue in d minor.
The key of E minor has one sharp: F sharp. It is the relative minor of G Major.