There are many ways to recover vehicles, and many toys (or tools) with which to do it!
I happen to like the simple elegance and speed of dynamic recoveries with a snatch strap. The tried and true way to attach the strap to the pulling vehicle is with a bow shackle, although soft shackles are certainly an option. I have always been told NEVER snatch using your tow ball, unless you want to see a towball flung at speed through someones windscreen (or head). Hence I slipped out the rather heavy (solid steel) standard Ineos towball from the Hayman Reece type receiver and slipped a Shackle Hitch from George 4×4 into place. Solid machined aluminium – so lighter than the steel towball but more than tough enough (20000kg breaking) to pull out anything I’d be game to try! Can be rotated so the shackle is horizontal or vertical. Just remember the bolt underneath (16mm head) that is there presumably to stop rattles. Useful note: the receiver is 140mm deep.
Always a good idea to zip tie everything in place too, so nothing shakes loose.
There are MANY options of hitch to choose from – including nice ones designed just for soft shackes.