How can I make the labels in Thunderbird visible to everyone who has the same boxes connected as me?

Question

Mail client

Hello!
How can I make the labels in Thunderbird visible to everyone who has the same boxes connected as me?
The situation is as follows, we have a common [email protected] mailbox at work, all letters are poured into it, and then the manager answers, only another unoccupied manager does not know if anyone took the incoming letter to work and he has to ask.
They wanted to put marks, but only the one who put them sees the marks ... Which creates significant difficulties in the work.
Maybe someone knows how to solve this problem or advise a free mail client that implements this function?
I hope I explained it in an understandable way, thanks!