The idea is to entangle all the photons of a star? All the photons in a narrow band?
From another star you can not magically distinguish the entangled photons. You can only make some measurements, and compare it with the measurements of the photons are entangled with, and get some correlations.
For example, you can create a pair of entangled photons in A, send one of them to B. In B the other person/alien can "transfer" the entanglement to a thermal photon from B and send it to A. Now in A you can measure the polarization of the photon you saved and the photon you received from B. Depending of how the other person/alien "transferred" the entanglement, you will get the same or opposite results when you measure the polarizations. So B can use "same" or "opposite" to transmit a bit of information to you.
The difficult part is to pick the correct photon in with a star making a gazillion of photons in the background.
You can create a gazillion of pairs of photons in A and send one half of each pair to B and get later the photon form B. But you must match exactly each received photon with the correct photon of the other half of the pair that you stored. Matching the wrong photon will produce only random noise.
IIUC the idea is that B will not entangle one photon but a gazillion of photons. It is possible to create in B an entangled state where the photon stored in A has the same or the opposite polarization of a gazillion of photons in B and send them. So now it would be easier to pick one of them.
The problem is that someone E in the middle can also look at the photons. Without the photon stored in A, the other person E can only measure random noise, it's impossible to know if B was transmitting "same" or "opposite". The problem is that the intermediate person E will see that in the polarizer all the photons pass or not pass together, never 10% of them pass and the other 90% don't pass.
The intermediate person E will see that half of the time all the photons pass and half of the time all the photons don't pass. This is a clear sign that the photons are entangled. So the secrecy of the quantum communication will be broken, in spite the content will never be discovered.