I found it on a few places, but no official adoption date, no order numbers, nor a license to manufacture them, nor a rifle replaced them. so I don't know what to think I've seen a lot of Danish rolling blocks, but the authors keep switching between calling it Dutch an Danish, did the Danish sell them to the Dutch? Or is that just them mixing the two up?
Remington was making the Rolling Block rifles found in the hands of the Danish, Spanish, etc. Very much focused on military contracts, they worked quite hard to get their rifles into the hands of every possible government buyer, and it's quite likely the Dutch tried out a few in the 1870's, along with other systems. But as far actually issuing them to an army, no. The Dutch seem to have moved pretty much directly from using a Snider conversion on their muskets, starting in the late 1860's, to having the French armory at St Etienne make them their bolt-action Beaumont rifles in the 1870's. Nor does it seem there's any similarity in the Danish and Dutch ammunition ( oddly, 11.3x50Rmm Beaumont seems to be rather close to 11.43x50Rmm Egyptian- but that's a long way to Denmark) . So, it does seem likely that, outside of someone finding a few test rifles, the names are just being confused.
For what it's worth, there's a useful site on the Beaumont and other Dutch rifles here