Access issues to HA green from within Mesh Network (Fritz Box)

Dear Community, as I had an earlier problem resolved with hints from you, I am trying to get another one solved, hoping to be successful again:
In my home I am operating two Fritzbox 4060 which create a mesh WiFi. One of them (the mesh master) is connected to the internet (by wired LAN to a router). The two boxes communicate wirelessly but both of them do also have physical LAN ports. I am using one of these ports on the “slave” box to connect my HA green. I am connecting to the HA using the HA app on my iphone13. So far so good. Its is working fine unless I move the iphone into an area where the WiFi of the master box is stronger and the phone obviously connects there. When this happens, I cannot connect to the HA green any more. The app doesn’t connect to the server and after a while I get a notification that it doesn’t work.
I have a desktop PC connected via LAN cable to the “slave” box, and from there I can access the green by typing IP adress and port without any problems.
I tried to fiddle around with the WiFi settings of the iphone, but nothing really helps. Sometimes, when I switch to another WiFi and back, or when I reboot the iPhone it works, but so far I have taken no notes to replicate what exactly needs to be done to make it work (should do this perhaps, so that I can be more precise here). My wish is to seamlessly have access to the green, whenever my phone is in the range of the mesh WiFi.
May I kindly ask for help from the community?