My wall is broken!

[mossy1200]

more pics.... It is definatly on a join, and the jib on the jeft seems to be furthur out than the jib on the right making a nonflush join.

You need to measure the internal distance of the fridge recess then the distance of the other side of cupboards.If the recess is deeper then they have removed some of the wall for the fridge making it weaker.

[mossy1200]

Not 100% sure

If so looks like with the gibstop coming out that the force was from the fridge being knocked back onto wall.This should not have caused damage in the room if the wall was full strength.I would assume the studs have been removed and smaller batterns have been installed to maximise the cavity size.

[Coldrider]

Having seen the last four photos.........
Is the fridge yours, if yes, you have merely contributed to the problem when installed.
If the fridge is the landlords it is not your problem.
Looks like a shonky DYI effort is the heart of the problem, the fridge should have been restrained from pushing back into the gib.

[nothingflash]

I dont want to loose bond or replace wall.

Put a mat or a pot plant on it