Wireless routers can have firewalls, routers can limit the size of files transmitted.
Routers can use DNS services like OpenDNS that block sites and ports.
Examining the DNS websites used may help explain the symptom.
Using a manual DNS setting may help.
If you do not have control over the hardware, do not use that location.
Can you set him up with remote desktop access for testing purposes? If he doesn't have issues when using remote desktop access, this suggests an issue with his computer (Is he using FileMaker Pro or a web browser to access the database?) Sometimes a reinstall of FileMaker on the client machine can solve the problem, but issues with user accounts (try setting up new account as a test) or the hard drive (check with a utility) or even other software can, in some cases be the cause of the trouble.