Hi @jonast ,
Don’t know the answer but perhaps you could check if the WLAN card is seated securely etc.
Here’s the [https://files.eetgroup.com/Brother/Parts%20Catalog/pl_BHS15_STD_e_ver4.pdf|parts reference list] for the printer.
On p.13 it shows the location of part #16 which is the WLAN card.
On p.14 the part number is shown for part #16, LT3808001.
If you think that the WLAN card may be faulty, search online using the part number ''only'' in the search term of your browser to get results for suppliers of the part.
Hopefully a start.