After making my previous post, I found a picture of the rear panel of the Prologue 3, which shows it as having a pair of tape out jacks. So you apparently CAN select one of the other source components which may be connected to the preamp, and have its signals routed into the tape deck for recording.
However, you have to be very careful about that. Since the preamp has no tape in jacks, and no tape monitor switch, you can only route the outputs of the tape deck into the preamp's aux or other line-level inputs. If you were to select that input on the preamp, the tape deck's output would essentially be routed to its input. If you then had the deck's monitor switch in the source (non-monitor) position, you would have a feedback loop that would put an extremely loud oscillation into your system.
So if you want to have the deck's record inputs connected, be absolutely certain that you only select the tape deck's outputs on the preamp's selector switch when the deck's monitor switch is in the monitor position. If you don't plan on doing any recording, it would be best to leave the deck's record inputs, and the preamp's tape outputs, unconnected.
Regards,
-- Al