Looking at the state of the existing group gasket and screen, I would be surprised if they have ever been replaced.
The gasket is brittle and cracking and the screen is so blocked, I doubt if that has ever been backflushed either.
With a new gasket (dimensions 73mm x 56mm x 8mm) and a replacement screen, the fit of the portafilter should be much better and there will be no chance of rancid off-tastes from the old coffee deposits.
An alternative to screen replacement is a long soak in Puly Caff.
Whilst you are cleaning, it is worth removing the centre screw and spray divider in the group. This was cleaned with Pully Caff, then a brass brush and a screwdriver were used to gently remove any remaining deposits.
Finally, the Azkoyen shower screen and gasket are in place. In fact I used a Faema E61 gasket here (common to many makes of machine), which fits okay and the portafilter handle seats well, although you need to exert some force to get it to seat straight out from the machine. I think this will ease over time.