Tool to use when going from exchange email to gmail

Save whatever information you want from outlook into a .pst.  You then use the tool to import the .pst into gmail.

 In Outlook click on File tab, Open and Export, Import/Export. In the Import and Export Wizard select Import from another program or file then click Next. Select Outlook Data File (. pst) then click Next. 

https://tools.google.com/dlpage/gsmmo#

https://support.google.com/a/users/answer/181236?hl=en