Thank you POGO 1104 for your reply.
I installed Thunderbid as you advised, here is the situation.
Smartphone/Thunderbid: I send an email “Test 1”, it is on “Sent Items” in Thunderbird". On PC/Outlook: Inbox: OK - Sent items: KO
On PC/Outlook: I send a mail “Test 2”, it is on “Sent Items” of Outlook Classic. Smartphone/Thunderbid: Inbox: OK - Sent Items: KO
Results NOT CONCLUDING!