OK,
From one complete side (as an ATCO) to the other half side (as a Pilot's Assisitant).
Yes, absolutely EVERYTHING is recorded on a FPS, complete with ticks when something is read back correctly, or as a record of having passed an airborne time to Radar.
From the P'sA side:
"Wow, that's neat..."
"Sssshhhhhhh!"
Read back everything.
"So, what's that symbol then?"
"We're cleared to join controlled airspace at such-a-level."
"Right."
"So what do YOU put?"
"Well, if I have time, a big "C."
"If you don't have time, then what?"
"Just remember it."
That's a single crew ops scenario.