Should we remove an email from Sent Mail after it is moved to Inbox? [on hold]

I am designing an employee management web application which has a built in email functionality which would be used by the employees to send emails.

Requirement

Once the user selects an email in the Outbox or Inbox, s/he should be able to move it to Inbox/Folder.

Problem

Gmail: The email is only copied to Inbox from Sent Mail on clicking the button Move to Inbox and on deleting the email form Inbox it is being deleted from both Inbox and Sent Mail. But, on using Move to option in Inbox, the email is completely moved to a folder.

Yahoo: The email is completely removed from Sent Mail on moving it to Inbox or a folder.

I'm confused seeing this difference in behavior. What are the advantages and disadvantages of each option?