Hello and welcome,
@Leijon - and sorry for your loss.
Seamaster experts will chime in as they read this, but on the basis of these photos this does look like a genuine Omega Seamaster from the 1960s. I am not an expert though, so I would wait for other opinions.
One thing that will help the experts is better photos of the watch in natural light, with the dial face on and the Seamaster text fully revealed. A picture of the crown on the side would also help.
The exact model can be determined by having a watchmaker open up the back. The reference number will be on the inside of that caseback.
It’s a lovely heirloom and one that is very wearable (can be dressed up or down), but before you do, it will need a service with a good independent watchmaker (not some guy who changes watch batteries in the mall!). That will ensure worn parts are replaced, the innards are fully cleaned, relubricated and the timekeeping regulated. It can then be worn without fear for a good few years to come. If you post your location, some members may be able to make a recommendation. Cost of service varies, but I’d say roughly $200-300 depending on location and what needs doing to the watch.
If you are not looking to keep but to sell, don’t do anything with servicing and list it on eBay. It will find its natural price.
Best of luck!