Sent as another alias not saved in Sent folder (Gmail)

Hi, I have two gmail accounts and the primary account A can send an email with the alias of the slave account B. The setup was done on the web settings of the gmail account A (“Send mail as:” by setting the smtp server with the gmail account B’s credential).

The eM Client has the credential of the gmail account A only and well shows the alias of B, which is auto-synced, when new mail is written. The problem is, when I send an email using the alias of B, the sent email is saved in the Sent box of the account A, as expected, but not made a copy in the Sent box of the account B (confirmed on the web). When I send an email with the alias of B on the web logged in with the account A, it is saved in both the Sent boxes of A and B.

Is it a intentionally designed feature? If not, how can I make the behavior the same as sending on the web?