To solve this problem I tried several things. The first thing was to check the settings of the modem but there was no option for port forwarding or disabling proxy settings. So I checked the steam forums for ‘steam update T-Mobile’, ‘steam T-Mobile’ etc. and found several threads describing a similar problem / exact problem.
On the first attempt I reinstalled steam but the client still said ‘no connection to the update server’.
On the second attempt I changed the client download location to different location (US, China etc.) but still ‘no connection to the update server’.
After working through all posts in the different threads I found the essential posts:
‘You have to change the modem setting to no proxy’
‘The no proxy setting is not possible on the Huawei B593 - so I just downloaded cyberghostvpn and use it just for updating/downloading games. Disable the vpn if you play the games’.
This post saved the day and since then my friend can update his games again.