From what I can find I'm not sure I can give an exact answer to the main question (when J&B started using screw caps) but I think I found something that matches your description, from 1972:
As far as I can tell the label matches the picture on the page you linked and appears to have a screw-cap.
Also, on the website you linked to, there are example bottles from the 60's and the 70's. Interestingly though, the 70's bottle has a different label than the one above from 1972.
Given all of this, I would assume the switch to screw caps happened in the late 60's or early 70's and that the bottle your friend obtained is likely from the same time period.