How does Teshigawara create the recording
The loss of memory applies to the existence of the extra person. Teshigawara and Mochizuki forgot about Reiko's existence, but they didn't forget the fact that they were working alongside Sakakibara and Mei to repel the curse looking for the extra.

Since everyone realised that the curse stopped (because people stopped dying), they should have concluded that the Extra died, whoever that was.

It's just reasonable that, after Sakakibara and Mei killed Reiko, they explained the situation to Teshigawara and Mochizuki, who of course believed them despite the lack of memory. At this point, it wouldn't be surprising that Teshigawara would be capable of making a recording with the warning.