How replace barrel on door lock on 1997 ford/jaguar/db7

[GretchPlayer]

I need to replace the barrel on the door of my DB7. It's a ford part and also used on jaguars.
I have a new barrel (see pic)

and have removed the door card, see pic of the inner side of the door lock.


Do I just slide the part arrowed in the pic downwards? Or is there more to it?

PS
I've replaced the boot lock - that was a simple job of sliding something similar.
And I replace the steering lock - impossible, till I watched a youtube video - then easy ;-)