If the mail messages are resident on one of the mail servers you are using, then they should be visible from a Mail.app mail account configured to reference that same mail server.

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Delete emails in Mail on Mac. You can delete email messages that you don’t need anymore to help keep your mailboxes manageable, and to free up storage space on your Mac or on the mail server.Deleted messages are available until they’re permanently erased.

For each imported mailbox, Mail creates an Import folder in the On My Mac section its sidebar. For another Mail tip, learn how to use Markup and Mail Drop, two new features added to Mail with OS X. 4) In the 'POP Download' section, choose the option 'Enable POP for mail that arrives from now on'. Doing this stops Outlook or any email clients from downloading old emails. Rather they will download emails from the date you select the option in step 4.

• Delete attachments that you saved.Choose Message Remove Attachments; the message remains in the mailbox and Mail indicates attachments were manually removed. For IMAP accounts, be sure to download the attachments first—attachments are deleted from the mail server and can’t be retrieved. Empty your Trash mailbox.
• Restore mailboxes and their content in Mail on Mac. If you set up Time Machine to back up files on your Mac, you can use the backups to restore lost mailboxes and email messages. See Restore items backed up with Time Machine.

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Those messages are resident on the server and not on the client box, which means there's no mail message importation that will be performed.

Are these mail messages possibly located in one or more different folders on the mail server (other than the inbox or suc)? If so, see if the folders are visible in the left column of Mail.app (in the default 10.7 three-column layout), and see if there's anything in the folders.

If all the accounts are set up and there are no different folders in use (or no messages in the folders), then select Mailbox > Rebuild from the Mail.app menus, and see if the messages appear. I've had that clear up some odd Mail.app misbehavior.

Jul 6, 2012 4:25 PM

Mail User Guide

You can delete email messages that you don’t need anymore to help keep your mailboxes manageable, and to free up storage space on your Mac or on the mail server. Deleted messages are available until they’re permanently erased.

Delete an email

1. In the Mail app on your Mac, select a message.

2. Click the Delete button in the Mail toolbar or move the pointer over the message’s header, then click the Delete button that appears.

   Tip: To prevent the next message in the list from being automatically selected (and marked as read), press and hold the Option key when you delete the message.

If you set the “Move discarded messages” option to Trash in Viewing preferences in Mail, you can delete a message by swiping left on the trackpad with two fingers or by moving the pointer over a Mail notification, then clicking Trash.

Delete multiple emails

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1. In the Mail app on your Mac, select messages or conversations in the list.

   All of the messages in a conversation will be deleted.

2. Click the Delete button in the Mail toolbar or press the Delete key.

If you delete a mailbox, all of the messages in the mailbox are deleted.

You can search for a set of messages to delete. For example, you can search for messages dated August 1 through September 5, 2018 by entering “date:8/01/18-9/05/18” in the Mail search field. Or, search for messages from a specific person by entering a name in the search field. Then select and delete the found messages.

View deleted emails

Whether you can view and retrieve messages after you delete them depends on how you set options in Mail preferences.

1. In the Mail app on your Mac, choose Mail > Preferences, then click Accounts.

2. Select an account, click Mailbox Behaviors, then check the setting for the Trash Mailbox option.

   • If a mailbox is specified: You can view deleted messages in the Trash mailbox until they’re permanently erased. To retrieve a deleted message, drag it from the Trash mailbox to another mailbox.

   • If None is specified: Deleted messages are removed and aren’t available in the Trash mailbox.

Permanently delete emails

In the Mail app on your Mac, do one of the following:

• Choose Mailbox > Erase Deleted Items, then choose an account.

• In the Mail sidebar, Control-click a Trash mailbox, then choose Erase Deleted Items.

You can set the “Erase deleted messages” option in Mail preferences to have Mail permanently erase deleted messages for you at a specified time. See Change Mailbox Behaviors preferences.

If you mistakenly delete messages, just drag them out of the Trash mailbox to another mailbox. Or select them in the Trash mailbox, then choose Message > Move to > [mailbox].