I understood the whole story up until “now my ex is mad at my son…”
Understood that this was a very special bike for racing, because you feel your son could benefit from that. Understood that he didn’t ride it for some months because of an injury—did he not even look at it? (I’m curious about the timeline—when was the theft discovered and reported to insurance?)
I also understand the things that you imply but don’t say: friction between ex and new husband; likely guilt at not being present more often in your son’s life, and the inevitable disagreements between ex-spouses.
If you want to send some of your own money to cover half the cost of a new bike, then your husband shouldn’t be the least bit angry. He can be ‘bemused’, shake his head and say nothing—or he can be ignorant of the whole thing. If I were you I would ask the ex a few pointed questions:
1. Where and how is the bike stored? After all, this isn’t a bike that your son is going to ride to school or to the grocery store. So it’s either in use in practice or race sessions, or it’s locked up, right? So how was it stolen? (This might not change my desire and intent to replace it, but I would want assurance that I’m not pouring money into a hole.)
2. Has your son thought about any of his friends who might fit the bill for what @escapedone7 suggested? Would he confront or accuse a likely thief-friend?
3. What was the insurance settlement, anyway? If you’re going to front half the cost of a new bike—and I gather that money isn’t the issue here, so you’re considering that—then the full amount of the settlement should go to you, and then you use that plus whatever else you think is fair to get to “your half” of the replacement.
4. And before you do any of that I would have a chat with my son about his personal responsibility for:
a) storing his things and checking on them occasionally even when they’re not being used;
b) letting adults know promptly when the thing turns up missing—and especially you, since it was your gift in the first place;
c) sometimes mommies and daddies don’t get along like they once did (I have a feeling you must have already had this talk; your ex sounds petty and vindictive, even if I give him some of the benefit of the doubt from only hearing your side of things), but that doesn’t mean you don’t love him—but you can’t keep making gifts like this materialize out of thin air, and
d) because of c) above, it is important for him to maintain some privacy in the communications you have with your son.
Good luck, dear.