On the Mac has long added all his accounts to the mail, how can I transfer all this to the iPhone?
Data on the added mailboxes does not migrate between devices through iCloud. On one device, they can be used for mail, on the other to synchronize contacts, and on the third – for both.
There is no difficulty adding the same entries to the Mail application on the iPhone and you do not need to install a separate program for each service.
Just go to Settings – Mail – Accounts and duplicate all the settings from your computer.
You can go the other way and configure the collection in almost one account, for example, in iCloud. The service does not have standard tools for this, you need to go from the other side. In the Gmail settings, you need to add redirection to iCloud for all letters or for a specific category of messages (through filters). So all mail will be in one account.