1. If you don't want the Orders History sidebox enabled, you can turn it off in Admin->Tools->Layout Boxes Controller.
But don't assume the user is re-placing the order via this method, without actually contacting them and confirming that that's what they're doing. Always verify with your users first.
2. If you're using the AIM module for payments, then the customer's order will ALWAYS be added to their order history if payment is correctly received. ("Correctly" means: no PHP errors due to bugs added by customizations or plugins or template/javascript alterations, no 'user error' by re-submitting payment forms multiple times)
My point here is: the AIM module doesn't do any temporary saving, and doesn't require relying on 3rd party steps to store the order separately.
The only exception would be if your site (template, javascript, customizations, plugins) is allowing users to actually re-click to re-submit payment before the previous click actually finishes. The default template already prevents duplicate-submission.
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