Missing part of roof joist

[JackT36]

We recently got a dormer installed on our roof but during construction, they noticed that the roofing joist on the right side it is on ends early.
The problem now is that the cross beam they installed is quite far inward. This causes there to be only about a cm of clearance between the beam and the window.
So now we cant easily finish this.

Can a beam be installed across the entire length of the house underneath the dormer? would this take the weight? Or any other way we can semi-easily solve this?

Added some more pictures for context.

 

[^woody^]

Jesus ... why is that cill area so wide?

You need your building inspector to have a look at this and see if he approves

 

[catlad]

Yes none of that looks good!

 

[RandomGrinch]

Why didn't they just sister the short rafter, down to the wall plate?

 

[DAZB]

There is just so much wrong with that set up...
1) the right hand rafter has been cut short, so what is supporting it ?
2) it should be a double rafter, might want to check if it is. (same other side too)
3) what exactly is going on with the "membrane" they have used ? it looks like kitchen roll
4) why is the front beam not sat directly below the window and supported down to joist level ?
5) what IS holding up that front beam ?
6) why is any of that front section even there ?
7) why does the top of the small diagonally cut rafter look like a dog chewed it ?
8) what is that product used on the underside of the slope ?
9) were any actual fixings used in this job or was it all just fixed with expanding foam ?
10) How much foam can one job take ??? was it Buy 1 Get 4 Free or something ?