From the Terms of Service:
Basically, you may use any computer as long as no one else has ever had or will ever have a FC account on that computer. You may access your FC account from any computer with any IP address provided no one else has an account with that computer or IP address. (you may use multiple computers and multipe IP addresses provided EACH PC/IP address has only one FC user on it.)
That is why they emphasize NOT using a public computer or the computer your referrer uses. The latter obviously has another FC user; the former might.
So: once you have set up YOUR internet connection in your new residence -- it can't be a "public" connection -- you just access your account and enter your new email address.
If you are going off to college or entering a retirement home and all they have is a public internet connection, you may be out of luck. I suggest you contact support about your situation and see what they recommend.
I was considering entering a retirement complex and discovered all they had was community IPS and I decided to stay put rather than risk losing all of my PTC/Survey/GPT accounts.
Copy of the TOS (red letters - my emphasis)
iv.Users must not create more than one account per person, nor may they create more than one account per household. A "household" is defined as a single dwelling (including basements, attics, extensions, etc). Should a user be a member of more than one household, he/she must be the only FusionCash user in each of those households.
v.Users must not create more than one account per computer or internet connection.
vi.Users must log in and use FusionCash on their own personal computer and internet connection only. The use of a FusionCash account on a public or shared computer, or public internet connection is grounds for disqualification. You may not access your FusionCash account on the same computer or internet connection as your referrer, referral, or any other FusionCash user. Violation of this term may be considered grounds for disqualification of any and all users involved.