If you would like your SRO timeline to be printed along with the invoice for the customer you need to enable this feature by going to: Admin > Company Setup > Global Settings > then enter "service" in the little search box on the top right of the Global Settings tab.
Change the Value to Y.
Note, all other workstations will have to quit out of CheckIn and go back in to take advantage of the change.
FYI. You may see another print dialog box depending on your settings popping up after printing the invoice as this is a separate print layout that the invoice and may also print on multiple pages.
*(This customer facing timeline will not show work/internal notes)
