It was originally written about in M. Hamidullah, "Some Arabic Inscriptions Of Medinah Of The Early Years Of Hijrah", Islamic Culture, 1939, Volume XIII, p. 438.
Do historians consider this to be actually written by Umar, and correctly dating to 625AD?
It is probably not in fact the oldest Islamic inscription nor likely written by Umar; that honor goes to the inscription of Zubayr, dated 24 A.H. on the basis of it naming the year Omar died. Reading the reference you provided, it seems like the inscription it talks about is an authentic early inscription but misdated; the wording of the inscription suggests a generic votive graffiti invoking the honored name of Abubakir and Umar rather than Umar's actual handwriting.