Although this is a klugy workaround, it might save you a bit of time. If you are referring to the assignees (Assigned to field), assuming that every task has an assignee, the easiest way to do this is to go to grid view and select the column of assignees, then go to your new copy, select the first of Assigned to task, and paste. It should populate all the assignments, but with 2 caveats:
1. Every field must have an assignee, or the ones that don't will be ignored, and the next assignee will be put in its place
2. If there are Summary tasks, the assignee field is not recognized as the same format and will error out without finishing assignments. In this case only the tasks of each Summary can be done at once.
Or Kluge 2:
You can align the columns of P4W fields in grid view to match the Project Desktop fields (or vice versa), then copy/paste the matching plan fields directly into Project Desktop's matching fields, including duration, etc. (potentially better outcome pasting first into Outlook or MS Word, etc. and then copying from there).
Caveat: Any Summary tasks will likely have to be outdented (or its sub-tasks indented, depending on your copy/paste).
Save the .mpp, then import the .mpp file into p4w from https://project.microsoft.com (if importing the project into the Default environment).
Or Kluge 3:
Same as Kluge 2, except instead of selecting/copying the plan items from P4W directly, choose "Export to Excel" in the ellipses (...) menu options to save to file instead, then copy fields from Excel to matching fields in Project Desktop.
The good news is once you have the .mpp file looking the way you wanted, you can put it somewhere where everyone can use it as the project template to import for each new project after that.
Hope some of that helps.