AVM Fritz!Box FTP Site for Firmware Downloads
The below FTP link is a shortcut to all the up to date Firmware’s for the below Listed AVM Fritz!Box models and recovery tools (images) 
http://ftp.avm.de/fritzbox/
fritzbox-3272
fritzbox-3490
fritzbox-4020
fritzbox-4040
fritzbox-5490
fritzbox-5491
fritzbox-6430-cable
fritzbox-6490-cable
fritzbox-6590-cable
fritzbox-6591-cable
fritzbox-6810-lte
fritzbox-6820-lte
fritzbox-6820-lte-v2
fritzbox-6840-lte
fritzbox-6842-lte
fritzbox-6890-lte
fritzbox-7272
fritzbox-7312
fritzbox-7360
fritzbox-7360-sl
fritzbox-7360-v1
fritzbox-7360-v2
fritzbox-7362-sl
fritzbox-7369
fritzbox-7390
fritzbox-7412
fritzbox-7430
fritzbox-7490
fritzbox-7520
fritzbox-7530
fritzbox-7560
fritzbox-7580
fritzbox-7581
fritzbox-7582
fritzbox-7583
fritzbox-7590
tools/
http://ftp.avm.de/fritzbox/