@TP-Link After the disconnection problems with my Mac I decided to reboot the Deco first. This was very succesfull! The Brother printer is again part of the network! pppfffttt thanks for your help.

@TP-Link Much Thanks for your advices, However the suggested measures did not solve the problem. But turn off of the 5 Ghz Wifi resulted also in a disconnection of the Wifi receiving on my MacBook...

With the firmware (1.4.0) the Brother printer was succesfuly connected with the Deco M5. That connecting process was only succesfull with this brother set-up wizard tool; all other possibilities...