Rolex 1803 president bracelet genuine??

[Burrost1]

Hi Guys, posted earlier about the stretch in my Rolex daydate bracelet, a few have posted saying to check it's genuine etc.. I ahev included the hall marks and end links as best I can
From 'CrownCollections' posts I can see all the hall marks are present and they are quite sharp, however on one side of the strap I can see the engraving 'M3' which I'm not sure what this means. The clasp looks a slightly different colour in certyain lights than the bracelet? Is that normal. It has '53' end links as well which are consistent with the 1803 it was taken from (and then put on my 1803)
Let me know what you think and also how to do check if the bracelet is real? I've been told the clasp could be ok but the bracelet could be fake??!!

Opinions and advice please!!!