I ask because I've always thought that the wave equation of the departing photon would be (barring nearby mirrors or absorbers) a sphere of wavelets growing out from the emitting atom at lightspeed. If this is the case, then the direction of the momentum isn't determined until the photon is absorbed, and that could be hundreds of years later. If the momentum is transferred upon emission, that would mean the photon somehow knows the direction of its eventual absorber? Or is the momentum only transferred upon absorption?
I imagine Heisenberg will be invoked, so I want the answer to deal with a concrete example: Imagine a powerful point light source at position A radiating in all directions. A basketball-court sized light shield (shout out to Webb) is at B, one light-second from A. The shield's material perfectly absorbs light, it is a perfect black. Another light shield of the same material, 4 times the area of the one at B, is at C, two light seconds from A and sqrt(2) light seconds from B (i.e. A-C is at right angles to A-B). The relative velocities of A, B and C are initially zero, and both light shields face A. At time t0 the light at A is turned on. Describe the momentum changes measured at A, B and C in the next 3 seconds.