That’s a 105.003 with a swapped caseback, according to the movement
and the dial (a common thing to happen back in the day at service before these watches became so valuable was a caseback swap). It’s difficult to see in that pic of your father but the hands look all white in it, which happened only from the next reference up from 2998. Still a lovely heirloom. Cherish it! And lovely pic of him
Edit: to clarify what I meant, but did not say, for posterity of those who can not infer it.
SN puts it in the range of 105.003-63/64.
Dial is for a 105.003 -> 2998/105.002 dials have minute track painted to the step in the dial, whereas 105.003 dials the minute track stops with a gap before the step (as in the watch pictured).
Fathers picture : clearly white baton hands in that picture (only found in later 105.002's onward).
Via occams razor thus...
Edit edit : if the silver rehaut is original (i think it looks silvery in the picture of your Dad) it may even be an early -63. It all depends on the 't swiss made t' (or lack of t) on the bottom of the dial, which is not visible due to the displaced nature of the minute track (and swiss made) away from the step, and the silver rehaut which has a slightly smaller diameter than the later black one (i think). If you can see the top of that from an angle, do post a pic.
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