Now line the strike plate up so that the the hole is lined up with the expanded mortise and draw a dot inside the two screw holes to mark where you'll be drilling.

Using a drill bit slightly smaller than the outer diameter of the screw, drill new screw holes in the door frame.

Most door frames are made out of soft pine, which means that the new holes will be very easy to drill. This also means that the surface tends to splinter when you first start drilling the new hole, which can make the new hole look ugly. Don't worry though - this will get covered by the striker plate once it's installed.