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Hello Gleeson, I attach an extract from 1949 Omega catalogue G590 which would appear to show your watch (which also appeared in earlier catalogues), a CK1122 with calibre 37.5....
To find a suitable watchmaker will require an effort and an expense - and it might be tempting not to bother and to do nothing. That would be a GREAT SHAME. Although the watch will probably run, after maybe many years without service/lubrication, the movement could well be damaged as a result.
I would NOT describe your watch as a ‘working man’s watch’ - those days were long past. This was one of the last pocket watches produced by Omega after decades of fabulous history. Although not cased in gold, this was a fine watch - and your son inherits it from his great grandfather! It will also have a re-sale value (but hopefully that won’t come into question). Please get it serviced properly - and then you have something to cherish long-term.
I hope that helps. Tom
Be sure to copy this complete thread for your son. With the family connection which should be sufficient to show him this is a significant watch, you now have a fairly complete background about the watch.
Add the sentimental worth to your newly discovered sense of the intrinsic worth, and your son might just go out and buy himself a new three-piece suit for his wedding, so he can wear his grandfather’s watch. AFTER it is serviced, of course!

Tom is a very meticulous reader - I had the pleasure to experience 😉