It is amazing to answer this simple question, so hard to find. I spent a lot of time finding the answer to this question in order to save minutes when creating a new profile. Well, then I never knew that it would take so long.
A simple hack is to copy the "PublishProfiles" folder from the previous project (where do you want to get the publication profile from) and paste it into the current project in the "MyProject" folder.
If you already have the "PublishProfiles" folder in the current project, then copy only the corresponding xxx.pubxml and xxx.pubxml files, user files from the previous project.
Then open the profile and edit it as you like.
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