[Решено] String translation plugin won't install due to memory issues

Background of the issue:
Dear support,

We're having issues installing the wpml string translation plugin in our new staging environment. We tried both via the OTGS installer plugin as well as via a manual download but without any luck.

We keep getting the "Fatal error: Allowed memory size of .. bytes exhausted" error even though our hosting company upped all memory to the max.

Can you help us out?

Symptoms:

Questions:
How do we proceed from here