EE sim in mobile router. Can a visitor who is not with EE use my connection?

[Crofter10]

I live in a remote area and the only mobile signal I can get is EE. I use it very well for the internet connection using my laptop and phone. 

I have a relative coming to visit for a week but he tells me that he is not on EE but another network which I think is 3. Will he still be able to use my router, using my password on the mobile router to connect to internet services?

[XRaySpeX]

@Crofter10 : Yes, you may let anyone connect to your router to be able to go on the Internet, with your consent but also at your responsibility in case they do anything untoward or unlawful. 

[bristolian]

Your mobile router is like any other wireless broadband (WiFi) network in this regard - anyone in range of it can search for and select the SSID (network name), and if they know the password, can connect to the internet using it.

[XRaySpeX]

Be aware that by connecting to your router he will be using your data with EE, not his with 3.