That's the same person as the ill-fated Constantine II – sometimes, a "Jr." is added to his name in order to more easily distinguish him from his father. And you're of course right about Licinius II. I bought this one because of the hilariously grotesque portrait – maybe the result of a failed internship program at the Antioch engraver's workshop? (Yet, it deserves some bonus points for Licinius' tiny hands. They kind of remind me of another, even less successful ruler.) Licinius II, Roman Empire, AE3, 317–320 AD, Antioch mint. Obv: DN VAL LICIN LICINIVS NOB C, laureate and draped bust left, holding mappa, globe, and sceptre. Rev: IOVI CONSERVATORI CAESS, Jupiter standing left, holding Victory on globe and sceptre, captive at feet left, delta in right field. 18mm, 2.82g. Ref: RIC VII, 29 delta.
If you combine the portrait itself with the roughness of his face, he looks like one of the undead from a horror movie.
Here's a Licinius II coin showing that, after the 1st civil war, he was very briefly renamed after his uncle. Licinius II A.D. 316- 317 21mm 2.7g VAL CONSTANTINVS LICINIVS N CAES; laureate head right. IOVI CONSERVATORI CAESS, Jupiter standing left, chlamys across left shoulder, holding Victory on globe & leaning on scepter, eagle with wreath to left; K in left field; wreath over X over A in right field. in exergue ALE RIC VII Alexandria 21
A good opportunity for some dynastic-commemorative issues from the two series of 325/6 for Constantine's vicennalia and 329 for Helena's funeral: Helena at Antioch in early 325, second phase RIC 61: Constantine I at Antioch in early 325, second phase RIC 57: Crispus at Antioch, in early 325 (or December 324), first phase RIC 53: Constantine I at Rome, in early 329 for the funerals of Helena, RIC 281: Constantine II in Rome, in early 329 for the funerals of Helena, RIC 282: