Based on other comments, and my own very limited knowledge of the relevant physics, there's no way to do this from Earth; all of the black holes (and binary block hole systems) are too far away for us to reliably aim a laser beam to slingshot around the black hole as is being described.

But the general form of what you're describing isn't any more outlandish than a time capsule, i.e. 'transmitting information into the future'.

But no, sorry, you can't see the past with the paucity of black holes near the Earth (and ignoring all of the other impediments to such a thing happening).