Michigan’s CPL application requirements state that an applicant must be a citizen of the United States, a legal resident of Michigan, and have resided in this state for not less than 6 months. But, if you have a valid carry permit from the state you are moving from, the 6-month waiting period is waived.
You are considered a resident of this state once you have obtained a driver’s license, personal identification card, or register to vote in Michigan. (see the complete statute for military residency requirements).
Michigan does not recognize permits from other states unless you are a resident of that state, so once you do establish residency here, your out-of-state permit is not valid for concealed carry in Michigan.