I had an experience like this recently although didn't realize it immediately. Prof from university where I did grad school. Hadn't interacted with him much but whatever, accepted his friend request and was surprised profile was fairly locked down. Then came the message at about 3 or 4 am, nothing much, a hi and a wave. Spammer was NOT what I was thinking and I was like really? 11th anniversary had just passed, thought that was fairly visible on my profile. Picked up on the faker aspect after I actually got a message with words.
I don't even know if he was purposely mimicking the prof or not. Name is common enough, image wasn't super clear, so while it looked like the prof a) haven't seen him in years b) it was the style of picture where it could pass for a lot of different people.