You might want to consider e-mailing your neighbor this video clip.
Alternatively, I’d scoop some up in a bag, leave it by their front door with a note saying, “Something that belongs to you was left on my property, so I am politely returning it. Next time you lose something similar and I find it on my property, it gets returned without a bag.”
If the neighbor’s dog is crapping on your lawn, it’s crapping on others. The HOA most assuredly has rules about pets, leashing, and cleaning up after them (if they’re even allowed).
For what it’s worth, many 55+ communities allow you to own property in the community, you just can’t (officially) live there. We were in that situation ourselves a few years back - bought a place for the in-laws to live in, but we couldn’t have occupied it ourself (well, I’m sure we could have moved in but couldn’t have used community facilities).
If you own the place, whether you live there or not should be immaterial. Get photos of the dog making its deposit, and file a complaint to the HOA. They’re more likely to take action than the city’s animal control officers, anyway.