The laws vary by state on how being convicted of a crime affects voting ability. In some states it makes no difference and you can vote from prison. In others rights are restored after you are released from prison. In others they are restored after parole or probation are completed. In others it is never restored, or only restored if the governor approves.
So if a person is convicted, arrested and serves a sentence in a state like Mississippi or Wyoming with permanent disenfranchisement, then moves to a state like Michigan which restores voting rights after a sentence is complete, how does it affect their voting rights? Would they be under Michigan’s laws or Wyoming’s laws? Does it matter if it is a federal or state crime?
The laws of the new state apply. Most of the states (perhaps all) that bar felons from voting enforce that for any felony conviction in any state or at the federal level.
This website has the details on the specifics for each state, including the actual laws.