I guess the author was making phone calls from the computer using something like Skype (recording in Skype began with version 8). And then the techie “smart” person did not realize they had record turned on in Skype when they made those calls. Sometimes we are so smart we are dumb.
I seriously doubt anything else put anything like their land line or cell phone calls on their old laptop computer, or had them in the cloud and mysteriously got them into the new laptop.
The only serious way they got to the new laptop was that they were actually there in the old lap top, and thus the back ups from it, and using something like Skype to make calls from the computer is the most likely way they got there.
Yes, the files were on his old computer. He said so. The conversations were not Skype calls. They were conversations he had around the house.