LR4 Moving a Cat and Photos from a PC to use as an Archive from External Drive on Mack

I use LR4 from my Mac laptop for over a year vs. using LR4 from my PC desktop where all my older photos live.    I want to copy/move my LR4 catalog and PC Photo files to an External Drive to be used as an Archive catalog/folders.

So my approach but I do not know if it is correct is;

Simply to copy my LR Catalog and LR Photos from my PC Desktop to the External Drive (exact same names).    Then I simply plan to use from the External Drive with my MBP.  I know how to transfer photos between these two files for future considerations.    I know the format of the external need to be one that my MAC can update.

I did not know if I needed to use LR on the Desktop to actually move the photos to the external drive?

Can anyone confirm or let me know what I need to do?

Thanks in advance.

--
Just an amateur
http://www.moosehead.smugmug.com