The answer is, be professional at all times.
So, yes. Provide them with the template that is owned by the company becuase he created it during the course of his employ.
And DON'T go crying to HR because his co-workers didn't give him a present. It sucks, but they didn't have to. Buck up and move on. Life isn't always fair.
IF (and there's always the possibility the slight was innocent) there was no speech and no gift becuase co-workers don't like your DH, him being petty and crying to HR and refusing to share templates isn't going to help the situation any.