Would it also be the case, that the mailbox itself has metal walls on all sides? That would block wifi or other RF solutions.
In an apartment building, the mailboxes can be outside. 6 wide x 6 high boxes (or some such) weatherproof enclosure. so no local power.
in such cases, you would not be allowed to drill holes and install an antenna.
My friends house in the mountains has their mailbox bolted to a wood plank with 10 other boxes. no HOA to dictate color or size or solar panel. etc.
Looks cute. That's why I queried a "roof" as an option. 
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A very good point. 
I tested this morning following you message @anon57585045 then I got signal about half the need distance & without the apartment wall ... so for now solution cannot be done at all. I m going to forgive it & think about something else & purchase needed parts
Sounds like you need a (much?) better radio device.
You have questions and so do we.
The idea can work but in order to help we need sone details
Are the mailboxes inside of a building?
If yes then what are the walls made from?
Can you add an antenna? Even a small one?
If you want to transmit when the door is open you may need to put a receiver so it can see the door.
It could act like a mesh network.
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