Here you can find a detailed manual how you can activate the SMTP authentification in Apple Mail.

1. Open the mail “Settings” via the menu:
   

2. Click “Accounts”
   

3. Under “Account Information”, click on “SMTP Server” at the bottom, and then on “Edit SMTP Server List”:
   

4. Click on “Extended”, and then on “Password” in “Identification”:
   

5. Enter the same access data as for the incoming server