Your request is easily solved via the addition of the site configuration parameter:
Add this parameter to Site Configuration tab from Site Admin console.
*Description: This parameter enables you to specify that the user who copies a record is listed in the specified User List fields of the copy. For more information on fields that have User List as their Field Type, see Customizing Project Entities. The value of this parameter is a comma-separated list of User List fields. For example, set the value of the parameter to BG_DETECTED_BY. Assume defect 10 is detected by user Cecil_qc, and user Shelly_qc copies defect 10. ALM creates a copy of the defect with Shelly_qc as the user who detected the defect, not Cecil_qc.*
When you add the parameter, the value will be the name of the field you wish for copy action to take ownership of. For example TS_RESPONSIBLE. Comma-separated list so add a comma and add whichever fields you wanted to be affected.