>Hmm, I haven't seen the 192.168.111.111\Michel syntax used in this context (although an IP address will certainly work for Remote Desktop). If you've found a case where that syntax works but the Laptop\Michel syntax doesn't, I'd be interested in knowing about that.

Yes, you are correct. If one works, the other one should work. I just pointed out that I tried both. For another laptop, I use the IP address for the authentication. So, I tried I would try that as well.