Every fingering that fits a hand
x665
easy
baax
easy
baa9
hard
What is true of it
F♯aug is F♯, A♯ and C𝄪 — 1, 3 and #5 counted from F♯.
C𝄪 is a double sharp, and it has to be: every letter from F♯ upwards is used once, so the #5 cannot be written any other way.
The easiest of the 3 fingerings below is x665: 3 fingers, held at the 5th fret.
None of them uses an open string, so this chord moves up the neck unchanged — the same shape 1 fret higher is the chord a semitone above.
1 string stays silent.
Where its notes are on the neck
The brass dots are F♯, the root. Everything else is a chord tone with its degree printed in it.
With a different note underneath
F♯aug/A♯
322x
F♯aug/C𝄪
x221
An inversion is the same chord with a different note lowest. The name changes to a slash name because the bass is what a listener hears as the foundation.