Hi Mario,
Check FM SO_DOCUMENT_SEND_API1, which you can send the mail directly from your dunning run.
If you want to send the mail directly after the dunning run, then you have to perform an activity in the following SPRO config-
IMG->Financial Accounting->Contract Accounts Receivable and Payable->Business Transactions->Dunning->Configure Dunning Activities.
In this, you need to define a activity type and assign the function module if you want to send the letter by mail.
Once you done with this config, you need to go to the following spro path-
IMG->Financial Accounting->Contract Accounts Receivable and Payable->Business Transactions->Dunning->Dunning by Dunning Procedure->Configure Dunning Procedure
In this activity, you need to assign the activity type that you have defined in the above config against the dunning actviity under the dunning levels under a particular dunning procedure as per your requirement.
You can fill up the content, receiver's email id and attachment (if there is any) and you can directly send it to the customer.
Hope it helps....
Thanks,
Amlan