Even though you invoke the maintenance plan as another user when it goes to interface with the file system it uses the SQL Server agent account.

To do this I would create a job and use a CmdExec step in place of your file share process where it is running as a proxy user, setup as your impersonated account.

here is how to create a proxy

https://technet.microsoft.com/en-us/library/ms189064(v=sql.105).aspx

*edited for clarity