It is no paradoxon.

Only your story is a bit unclear at the point where it matters. Let me ask a question to clarify = to destroy what appears a paradoxon, but isn’t.

Question:
Who controls the transmission of the information - the past self or the future self?

If the past self controls the transmission, then he receives no information. Case closed. It does not matter what the future self is doing.

If the future self controls the transmission, then he knows when the past self turns off the device. He can send it just a minute further into the past, before the past self turns off the device, and so the past self receives it “in time”.