Issue with leadscrew in Fimap Lathe

I have recently bought a used Fimap TP 20 lathe, which is identical to this one. I can provide pictures of my lathe if needed.

I'm a new machinist, and this is my first personal lathe. The machine works well, and I have been enjoying it. However there seems to be an issue with the threading process. The machine's leadscrew (highlighted in red) which is engaged when the threading lever is pulled does not rotate. I have been able to identify the problem, which seems to be a missing pin in this part. I can see the shaft from the machine rotate, but the leadscrew does not follow it. I think the pin has been broken but I cannot find the leftover pin in the shaft. The leadscrew appears to have also moved axially (I can displace it axially with my hand).

Does anyone here have a Fimap Lathe and do you think you could help with a close up picture or some sort of measurement, so I could figure out where the pin is or some tips
on how to solve this problem?

I don't have a Fimap lathe, but many lathes have the same design.

With the electric power turned off.

The picture of "this part". If the pin is broken try this.

Remove the end bracket on the right end of the lathe or Tail Stock end, then engage the 1/2 nut - threading lever-
(sorry seems simple English, but just trying to make it easier for you to understand)
then with the lever engaged and turn the hand feed wheel to try to pull the feed shaft out of the quick change shaft collar. don't turn it so hard you break anything but if it has moved a little before it should come out.

Ah that's great, I should be able to keep the shafts aligned like this. I will try to do this as soon as I'm back at the workshop.