What is true of it
D♯maj9 is D♯, F𝄪, A♯, C𝄪 and E♯ — 1, 3, 5, 7 and 9 counted from D♯.
F𝄪 and C𝄪 are double sharps, and they have to be: every letter from D♯ upwards is used once, so the 3 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 87a8: 4 fingers, held at the 7th 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.
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 D♯, the root. Everything else is a chord tone with its degree printed in it.
With a different note underneath
D♯maj9/F𝄪
0211
D♯maj9/A♯
3535
D♯maj9/C𝄪
7768
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.