Step 1: Export and Save Zimbra Emails in EML Format
Following the below-mentioned steps will let you save Zimbra mailbox items directly to EML format on your system:

Launch Zimbra desktop client and click on the Preferences tab.
Now, from the left pane, choose Import/Export.
From the export panel choose All Folders.
At this point, you can either select any individual mailbox item or the whole mailbox. Click OK to proceed.
Click on Export to begin the process.
Next, provide the destination to save the mailbox items.
The exported items are compressed in a ZIP file and are required to be unzipped. Use proper tools like WinZip/ WinRAR to unzip the file.
Next, check the extension of the unzipped mailbox items. At present, Zimbra only allows EML format for exporting the mailbox files.

Step 2: Migrate EML Files to Outlook
EML files can easily be accessed with the Outlook desktop client anytime.
Hence, it seems like overkill, but it is possible to migrate EML files to your Outlook desktop client.
Open your Outlook desktop client and select the Folder tab from the ribbon. Next, click on the New Folder tab.
Provide a new name for the folder.
One can now directly drag and drop all the EML mails into this folder.

Step 3: Export Zimbra Emails from Outlook to PST Files
It is now possible to export the Zimbra emails (from Outlook) as a PST file to your system.

Click to the File tab > select Open & Export from the left pane.
Click on the Import & Export tab. This will open up Import and Export Wizard. From the list, select Export to a file.
Next, select Outlook Data File (.pst) option.
Select the folder containing the Zimbra backup files.
Click on the Browse button to save the file to the desired location.
Check the prior assigned location for the saved PST file.