I think ActiveSync has a problem copying items from a PPC to a PC when a new partnership is created

There is an option for 'Merge Items' but it isn't very reliable. You would run the risk of A/S overwriting all your PPC stuff with the blank PC folders.
If you are changing PC's, then the best option is probably to open Outlook on the 1st PC, and use the File/Import & Export function to make a backup copy of your Outlook data (remember in the last screen to collapse the folder tree, select My Mailbox and tick 'Include Subfolders'); you can then copy the resulting backup.pst file to the new PC, then do a File/Import and Export/Import/Personal Folders File to import all your data to the new PC. Ensure that the imported data is all correct in the default profile.
Once that's done, connect the PPC to the new PC and create a partnership, during which the conflict wizard will ask you what to do- select Replace Items on My Device, and your stuff should sync OK.
You will already have the backup.pst file as a precaution, but I'd also suggest backing up the PPC just in case!