Combine mail from 10 mailboxes to have access to all letters from anywhere

Question

Email

I have about 10 boxes: work, personal, for registrations. There are 3 computers on which I work.
I want to make sure that all computers have access to all incoming and outgoing letters.
Now I have mail programs configured on each computer that collect letters from all mailboxes, but this is somehow not convenient.
Inconvenient: outgoing messages are stored on the computer, and since I write letters from 3 computers, then all outgoing ones are divided on computers, it is difficult to find a letter if you don’t remember where you wrote it from.
So far I have come up with only one idea:
Start a mailbox on google that will collect letters from other mailboxes, so I will get a common incoming archive.
But there is a problem: when answering, I will answer from the general mailbox, and not from the one from which the letter came.
Maybe there are some other ideas how to do it?

Answer 1

I use Yandex. works the way you want. I added other boxes to the box. You can reply from any address.
Recommend.

Answer 2

I advise Yandex for this, Google crookedly collects

Answer 3

In gmail, you can also configure to respond from any desired email