Bricking in is a favourite of mine. As you say it anchors it, it also improves fire resisting properties. Just make sure you get it exactly where you want it! Consider the door opening. I think you have a couple of drawers in the safe. Make sure the door can open far enough to allow those to operate properly. Also make sure you get it dead level so the door doesn’t swing open or shut and trap your fingers.
Once you have it bricked in and level leave it unopened for a couple of days so your cement has chance to set. It is easy to get it just so and then open the door and spoil it all!
