What is true of it
G♯maj9 is G♯, B♯, D♯, F𝄪 and A♯ — 1, 3, 5, 7 and 9 counted from G♯.
F𝄪 is a double sharp, and it has to be: every letter from G♯ upwards is used once, so the 7 cannot be written any other way.
On an instrument that cannot reach all 5, the 5 and 1 go first, in that order.
The easiest of the 1 fingering below is 1031: 3 fingers, held at the 1st fret.
All of them use open strings, which is what makes a shape quiet to change to.
It leaves out the 5. 4 strings cannot carry 5 notes, and the 5 is the one this chord can lose without changing what it is.
Where its notes are on the neck
The brass dots are G♯, the root. Everything else is a chord tone with its degree printed in it.
With a different note underneath
G♯maj9/B♯
x031
G♯maj9/D♯
8a8a
G♯maj9/F𝄪
0041
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.