If your routers wan port is ethernet it should work. You of course cannot plug a dsl or cable wan port into a modem.
You largest issue will be if the provider has any form of mac locking on the modem. You will need your router to have the same mac as the previous device... many times you can just reboot the modem and it will take the new one.
When I visit my friend who is willing to let me use her modem,wil I have difficulty using my router?
I would unplug her cable and use mine instead going thru my router to my laptop.