How to update a membership user account to become a CMS user account

Can existing Membership users be converted into CMS users? What's the best way to accomplish that?

The simple answer here is that no, membership users cannot be converted into CMS users. The reasoning behind this is that the CMS treats both groups very differently in terms of permissions and what they can and can't do with the workarea. 

The best thing to do going forward would be to create a CMS user account for the person and have them use that login instead of the membership one. The unique identifier is the "Username" so if you wanted to keep the membership account, just give the user a different username for the CMS account. 

If you're using Active Directory/LDAP:

Since the username cannot be changed, the above method won't work for you. Currently, the only way around this rule would be to completely delete the membership account and recreate it as a CMS user.