Import Email Messages in bulk and relate them to Cases

1. Create a .csv file with the following column headers:

• Parent ID
• From Address
• From Name
• To Address
• CC Address
• BCC Address
• Is Incoming
• Message Date
• Status
• Headers
• Subject
• Text Body
• HTML Body

Note: It is best to compare the column headers mentioned above with the fields in email records you currently have in Salesforce. By doing so, you will know what type of data (value) goes into the Salesforce fields. See also: EmailMessage | SOAP API Developer Guide 
 

2. Start the Data Loader and use the "Insert" function.
3. Log in with your credentials. Note that you may have to use a security token for this. Click Next after authentication.
4. Select the Show all Salesforce Objects box and select the object: Email Message (EmailMessage).
5. Choose the .csv file (the one from step 1) and click Next.
6. Click OK on the confirmation window indicating the number of records to be processed.
7. On the next page, click Create or Edit a Map.
8. On the Mapping screen, click Auto-Match Fields to Columns and click OK.
9. Click Next.
10. Choose the destination for the error and success files then click Finish.

Notes:

• This is only available for organizations with access to Salesforce API. This can be done if Email-to-Case is enabled.
• To import emails into the Activity History of other Salesforce Objects, please review Import Tasks or Events into existing records. 
• If you want to make the paper clip or attachment icon appear in Activity Timeline for the email that has a linked Content. Please add and set the 'IsClientManaged' field to True on your .csv file for Insert.
• If Parent Id/Related to field is not provided while inserting EmailMessage records they become private to the user who has imported them. Inserting Audit fields along with these records without parent ID will lead to an insufficient access rights on cross reference ID error.

See also:
EmailMessage

Support video:
How to Download and Install Data Loader