Consolidated email accounts

If the account is a POP account, the account's Inbox mailbox is stored locally on your computer's hard drive. Moving received messages from one account's Inbox mailbox to this account's Inbox mailbox does not place the messages on the incoming mail server for the account. In order for messages to be downloaded by a POP account with an email client, the messages must be on the incoming mail server for the account.

If this account is an IMAP account, moving messages from another account's Inbox mailbox to the IMAP account's Inbox mailbox with the Mail.app on your Mac will place the messages in the account's Inbox mailbox on the server. After doing so when accessing the IMAP account with the iPhone's Mail client, the messages will be available in the account's Inbox mailbox automatically. All server stored mailboxes with an IMAP account are kept synchronized with the server automatically with each email client used to access the account.