First, go here: http://www.state.tn.us/safety/handgunmain.htm
And look into the FAQ. http://www.state.tn.us/safety/handgun/handgunfaqs.htm
And, of course, there is nothing about a person moving into the state with another state's permit.
This said, try contacting the state directly, this is probably best to get the correct info.
Lisa Knight, Manager
1150 Foster Avenue
Nashville, TN 37243
FYI: It should not take the full 90 days, however, there has been a recent rush to get permits, which may impact the waiting period.
Another good source of info on this topic may be posting in this forum: tngunowners.com