I had to say this to my mom yesterday, when she was contemplating a gift for my sister who just lost her oldest dog (and me, who lost my precious cat Oliver to cancer a few months ago): when it comes to memorials, ASK FIRST. You don't know until you ask them whether something you're thinking of will just set them off/trigger worse grief, or otoh be really appreciated. Especially since they may not even know until a few days have passed just what hurts and what feels right. I can't look at an elastic hair tie without bursting into tears because Ollie loved to play with them, but it's just a stupid everyday item to most people. My partner can't look at photos of him, which is a common gift/memorial thing.

I would say, verbal condolences and space to deal are probably what they'll appreciate right away, but let them know that if they plan to honor him in some way, you'd be happy to pay for it, like a frame for a photo or a figurine or what have you. That lets them know that you're grieving with them and would like to honor him in a way that they feel is right for their home and their memories.