There is no need to transfer Office 2010 to the new PC. Simply transfer all the
data files you want (e.g. documents, templates, workbooks, pst files, etc.) and install Office 365 on the new PC. If Office 365 is already installed there, it can import your pst file without the need for a 3rd-party application. See:
Import email, contacts, and calendar from an Outlook .pst file - Office Support