I'm working on a story, and I need to know the following: If someone called a phone number from a pay phone, would the owner of the private phone have anyway (including phone company records) to find out the number and time of that incoming call 2-3 months later?

I would think years later.

My husband is a retired AT&T/Lucent 5ESS senior installer and says it would depend on the type of switching equipment at the phone office plus the locale (rural vs. city). If it's a city with the right switching equipment, yes, those records were on tape, would be a pain/effort to find, but could be found if court ordered.

What is the Country or area you are dealing with?
If you could tell a little more, we could give a little more.