I continue to inform you about the advancement of this issue, hoping some angel can help in solving this issue of Outlook 2013 (now I am convinced it is a real "bug").

The issue is related to the folder (I am not sure of the name in english) in which the rule copy the message.
When copying the sent message in the sent folder of :
- the personal folder, it does not work (the issue: draft message).
- the mailbox folder, it works (not draft message).



Complementary information about my configuration:
The principle of my rules that reveals this issue is the following.
The option "Save a copy of the sent message in the sent folder" is inactive.
- Rule "Send Customer1" : Move a copy in Archive/Customer1 folder of personal folder, and stop processing rules.
- ...
- Rule "Send CustomerN" : Move a copy in Archive/CustomerN folder of personal folder, and stop processing rules.
- Rule "Send all ofhers" : Move a copy in Sent folder of personal folder, and stop processing rules.
- Rule "Receive Customer1" : Move the message in Archive/Customer1 folder of personal folder, and stop processing rules.
- ...
- Rule "Receive CustomerN" : Move the message in Archive/CustomerN folder of personal folder, and stop processing rules.

Still no contributor

For information, I do not find any fix of Outlook.

I just set the unstatisfying workaround :

disable all rules "Send XXX" => no more sent messages saved as draft.