When you configure the submit button with a Submit Form action, you have the option of choosing to submit the form data (FDF, HTML, or XFDF), or the complete document (PDF). Choose FDF or XFDF if you want to use Acrobat to populate a blank form by importing the form data. Don't use the form distribution process in Acrobat or else it will change how the submit button behaves.
Bear in mind that if you send ordinary form data, the signature is lost. You can't just import a "loose" signature into a form, that would be a great trick for getting people to sign things they never saw!
It is possible to submit a signature without sending the whole file, but it's a rather complex process of sending an incremental update to a file.
So I've done the doc as xfdf and even though it still only saves and sends the form data it can still be viewed as a pdf with the new filled in content and printed nicely with the content. This is fine. Is there any expiration date as to how long this data can be view for? And just to confirm there are no restrictions on this plus the designer can use their copy of Arobat to create these forms, not the client? The client can also still view all the submitted forms fine if they don't have acrobat pro?
The only limitation is that signatures will not work.