French Montana Has No Problem With Iggy Azalea Moving On

French Montana's not fazed at all by Iggy Azalea dating a new dude ... because he's the one who ended their relationship.

Sources close to French tell us he wants Iggy to be happy, and has no issue with her hooking up with music producer Ljay Currie -- who posted a pic wearing jewelry French bought for Iggy. We're told it's no skin off French's back ... he doesn't care what she does with the diamonds.

As for the rapper's tweet about shooting someone's "punk Asss," which seemed to be a threat aimed at Ljay -- it had nothing to do with him.

We're told French was in the studio that day laying down a new track ... and the "threat" was a lyric.