Best way to reinforce beam for a deadbolt?
I would sister up another 2x4 inside of the existing stud (weird to see a single stud there anyway, usually you would have a stud and a trimmer). Secure it with screws along the entire length.

Use heavy bolts with washers from the opening/door side to the back side of the studs, above and below the strike plate/latch area. To make them sit flush on the opening/door side, countersink the heads.

Then install a heavy duty reinforced strike cup and plate unit, there are many types and sizes available: