Is this a pocket watch conversion or did it come from the factory this way? The seller claims it measures 40 mm and dates to 1915.Tthe serial on the movement backs that up but I've never seen anything like it through google. The crown is also very different to the colour of the case.

 

My opinion is that it wasn't made by Omega.

It seems that the movement (26.5 something) has been fitted to a Borgel style case and should have a screw on crystal/bezel/cover and back.

Most wrist watches at that time did not have the ultra wide strap that this one has, but it could well have been assembled in that period by a jeweller in the same way that pocket watches were, i.e., you picked a case that pleased you and a movement to go inside it.

I also find the dial, hands and numerals to be in amazing condition for a 100 year old watch.

 

Caliber is much earlier than a 26.5 and the case isn't Omega. Wristwatches from Omega in 1915 were usually either 33 or 35 mm with 12 or 13 lignes caliber. One exception with a less common wider 41mm case and a 15 lignes caliber.
Here the case size doesn't match the caliber size. the larger band style came later
I also confirm that the standard strap width was 12-14mm.
For those reasons I also suppose that the dial isn't original, but it's difficult to say based on pictures. If so it's well done. Is it enamel or painted?