1050 In An Old 955i ?

Its been done but its a lot of work.
The 1050 motors from 2005 up to about 2016 (I think) will physically slot straight in to the frame.

The 2001 was normally aspirated, the first injection was the 2003-04 model which was basically the mk1 1050 engine sleeved down to 955.

So you have to get over the issue of fuelling.
Your tank feeds carbs, the 2003/04 engine has two fuel lines with a flow and return fuel rail which pumps fuel back to the tank, the 2005 and on engine has a single fuel line with a closed circuit to the fuel rail.

Neither of which have fuel pumps that fit neatly into or onto your tank.

I'm fairly sure if you need to swap the ECU as well because I don't believe the ECUs for each engine recognise the other fuelling systems.

Which in turn brings other issues for instance the tacho drive is on your front axle (on the right side on the 2001?), but if you have swapped to the 1050 ecu, it wants the tacho input from the crankshaft. Which you can get around by making additions to the loom.
And I think you might need to change the clocks because your existing ones wont recognise the new inputs from the 1050 ECU

It has been done and if you scour all the various triumph forums you will find threads about it.
But its a rabbit hole you REALLY have to want to jump into