Your drawing helps quite a bit, but in the future a "post" refers to a vertical timber and a "beam" refers to a horizontal timber.

As far as your plans, its not a good idea. Screws or lag bolts have no reliable strength when screwed straight into end grain. You would be better off toe-screwing the lag bolts from top of the beam into the post. Your idea of using the "shelf" or shoulder cut into the post is a good idea and should be kept.

I would suggest using a free-tenon, since you don't have the length for real tenons. In conjunction with the free-tenons, the shoulder is a must and the lag bolts toe screwed wouldn't hurt.

good luck