My short answer, before.
Longer answer: I'm always working on merges, and I learned the hard way that bad merges take a lot of work to fix.
Ideally, I propose a merge for two identical profiles. Teflon coating for a proposed merge means finding sources for the facts and adding them to both of the duplicate profiles. I make sure I include relevant comments and sources from both of the duplicates and try to respect the style of both of the profile managers. Its courteous, but its also less work - there is no need for further edits or research when the merge is completed.
On occasion I have to work with one or both profile managers to get the changes made. Sometimes a person or a project needs a day or a week to digest new information about their ancestor, but then the merge is also more likely to be approved before 30 days, and less likely to be rejected.
If I only have access to one of the duplicates, then I do what Bruce suggests, build a complete, sourced biography so the correct information is obvious.