Provider or reseller wants to move existing subscription(s) between accounts in Parallels Automation.
In current implementation (from 6.0) Parallels Automation does allow vendor to move subscriptions between accounts. You can refer to the documentation to migrate subscriptions.
The solution which may be used for OSA 5.5 and below is to cancel subscription under the current account and recreate it from scratch under the desired account.
Important: keep in mind that customer's services may be physically destroyed if you cancel an existing subscription (depending on PA Service Plan/Template configuration), so use the solution with care. Do create backup of customer's services before cancelling subscription.