The first two Johns apparently signed their names in the same fashion, although it remains a very debatable point as to whether the earliest-appearing of the "John * Moll" (the star-shaped asterisk is typical) rifles is John I or John II. Some would add John III to the mix as well, although I believe his signature stands out as being executed a bit differently.
All I can say for certain is that, thus far, I know of two restocks which I feel clearly are John I barrels, as the signatures on those take the form of gigantic inlayed (gold) "JOHANNES MOLL." I also believe during or post-War he signed as "John Moll" as per your barrel, but so did his son and his grandson. So if I haven't confused things too badly, I'd say yours could be any of the three as I can't really tell given the damage to the signature. Looks like the more open I or II, the John III signatures to my eye are bit more cramped and less flowing, less stylistically accomplished.