FROM SOURCE COMPUTER:

File - Import and Export - Export to a file - Personal Folder File (.pst)

Select which folder you want to export and check "Include Subfolders" if applies.

Save to a PST file on hard drive or USB drive.
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TO DESTINATION COMPUTER:

File - Import and Export - Import from another program or file - Personal Folder File (.pst) - File to import

Go to the saved PST file.