Colm,
Many moons ago, I went through this process after I picked up an Adept lathe at a car boot sale for about £20, and decided to offer it to a model boat making friend of mine for him to make boat fittings with. I wouldn't consider either the Adept or Super Adept (as in Tin's photo) anything more than a basic watchmakers lathe where most of the work is done by hand graving. It just isn't rigid enough to do meaningful precision work.
I already had a small chuck like this one knocking about my shop, but now you would need to purchase one similar to this.
http://www.rdgtools.co.uk/acatalog/50MM-3-JAW-SELF-CENTERING-CHUCK-12MM-THREAD-29875.html
They have a few small chucks on this site to look at.
http://www.rdgtools.co.uk/acatalog/45MM_-_65MM_DIAMETER_3_JAW_CHUCKS.html
The lathe itself is now starting to cost you money, and in my opinion, just isn't worth doing as they are sometimes just given away between friends. If you sell in the US you can get all sorts of idiots wanting to buy it at inflated prices, but here in the UK, where we know about them, you will be lucky if you can get someone to take it off your hands for nothing. If it was in my shop, I would just chop it up in the hope I could make a small engine out of the cast iron. But in your case, with it being your father's, only you can decide if you want to make the loss.
Anyway back to what I did.
I can't remember the spindle thread size of the adept but I made a converter plate to go between the two different sizes. The plate was first screwed onto the Adept to face it off (a big and long job in itself), then held in soft jaws in my larger lathe to cut the new nose thread. The runout after doing it was less than 0.002" on a bar about 2" from the chuck nose.
If I was going to do it again, I would buy a chuck with a smaller mounting thread and bore the Adept thread into the back of it or just make a sleeve with the adept thread inside, and the new chuck thread on the outside (in that case you would need to buy a chuck with a larger thread hole). Or like in previous posts, just make a new spindle to fit a new chuck onto.
In all cases you need to find someone with preferably a lathe with good precision to do all the threading and cutting.
Send me an email or PM about your decision what you want doing with it and I will see if I can help.
I hope this helps
John