It's quite hard to find information on router / modem compatibility. I took a chance on a Megafon 150 advertised on eBay (Russia) as it was so much cheaper than anything available domestically. The Megafon 150 appears to be a Huawei E3372s M150-2. It has good frequency support (4G: 800/1800/2600, 3G 900/2100, 2G: 850/900/1800/1900).
I plugged it into the side USB port and it was quick to connect to the mobile network automatically downloading the necessary APN, so no need to manually configure the modem at all.
The Internet -> Mobile Telephone Network sub menu appeared in the FRITZ!Box configuration pages and I ticked the "USB Tethering" box and pressed "Apply" at the bottom of the page. Returning to the Overview page now showed:
If you return to the Internet -> Mobile Telephone Network page there is now an IP address you can use to go to the modem's configuration pages (Note it seems there's a FRITZ!Box bug that shows your DNS server IP address if set rather than the IP address of the modem).
Note you can only connect using USB Tethering. Direct mode does NOT work with the E3372s. [FYI I have had a ZTE MF821 working fine in direct mode]
Note also the FRITZ!Box configuration pages seem to refresh extremely slowly if USB Tethering is enabled - anybody else get that?
