What is true of it
B13 is B, D♯, F♯, A, C♯ and G♯ — 1, 3, 5, b7, 9 and 13 counted from B.
On an instrument that cannot reach all 6, the 5, 9 and 1 go first, in that order.
The easiest of the 1 fingering below is 4340: 3 fingers, held at the 3rd 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 and 9. 4 strings cannot carry 6 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 B, the root. Everything else is a chord tone with its degree printed in it.
With a different note underneath
B13/D♯
x340
B13/F♯
b9bb
B13/A
2340
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.