What is true of it
D♯m7♭5 is D♯, F♯, A and C♯ — 1, b3, b5 and b7 counted from D♯.
These are also the notes of F♯m6/D♯ and G♭m6/D♯. Which name is right depends on what is underneath and what came before — the notes alone do not decide.
The easiest of the 1 fingering below is 8999: 4 fingers, held at the 8th 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.
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♯m7♭5/A
2324
D♯m7♭5/C♯
6656
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.