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Replacing the Briggs and Straton 15.5HP for model 944.609850 with Briggs & Stratton 20Hp twin cylinder engine.
The 20HP comme from a riding lawn mower the mark and model is unknown.
Does any vertical motor from any riding motor fit my craftsman riding lawn mower??

Yes and no, it depends on how much fabrication equipment you have available.
If you're looking for a drop in replacement without breaking out a plasma cutter and welder, check the mounting profile; make a cardboard templet of either the new engine or mower base and compare. Also, the shaft diameter will need to be the same as the old mill if you need to reuse the pulleys. If it's a twin cylinder replacing a single, there might be clearance issues with the hood down, where the exhaust exits, fuel line routing, etc.

The mounting holes on most vertical engines are the same so motor will bolt in.
That is the least of you problems
Next is the shaft diameter & length
residentials are 1" & commercials are 1.125" if not the same you will need new pulleys and then the belts might not fit properly.
After the space constraints Dan mentioned there are wiring considerations including alternator output, you might need to swap out alternator stators.
The biggie will be the muffler as Dan also mentioned .
These are part of the mower, not the engines in most cases and will most likely need modification to be made to fit.
New ones can go as high as $ 200

Lawn tractor engine mounting should not be an issue. But is easy to check like flyerdan stated.Wiring,exhaust, bottom crank shaft length and O.D., throttle / choke cable length and fuel tank location , to name a few, can cause issues. Make sure both have carb solenoid wiring / or not. Main wiring connection can be a challenge. What really helps is have'n the complete tractor the twin engine came off of. On a scale of one wrench be'n easy to 10 wrench be'n hard. This could be a 7-8 wrench job. Do your home work .

I have a Craftsman LT-1000 917.275371, purchased May 2005, with 31C7070230E1 engine. In 2013 that engine died and I replaced it with a 31P677 0912 G5 purchased online, pretty similar engine, slightly larger, and the new engine had an oil filter too.

This was a straightforward swap, I'd say Level 2 effort/difficulty on scale of 10. I also saved parts like alternator, coil, carburetor etc., as spare parts. Really good thing was that new engine cranked and started tons easier, I always had issues with the cranking of the original engine, even with new or tested battery and adjusting the valves as per instruction. And like the oil filter too, as my mowing is in dustry arizona for weeds like tumbleweeds, not a Kentucky lawn.