I’d at least check the gun for fingerprints and his hand for residue.
No foolin'! And check the (former) boyfriend's nose to see if it's grown since he told that story.
I'm sure the authorities will do exactly that, but real life is not like CSI.
If he handled the gun previously, say, at the gun shop where it was bought, his fingerprints will be on it. Were her fingerprints over top of his or vice versa? I suspect his hands were larger than hers, too. That gets down to interpretation.
Also, a gun fired in an enclosed vehicle is going to leave GSR everywhere. So then you have to look at patterns. Again that involves interpretation.
None of this is cut and dried.