From my POSTFIX mail server I want to send a mail directly to an existing account.
Then you need SPF records. But I can only say this again - don't do it
You WILL be in pain, as nobody will take your mails from you.
Many large providers will complain around asking you to sign up for their weird whitelists, and many small providers use very weird RBL lists that will block you for no reason, often asking for money.
SMTP is broken, and there is nothing you can do about it.
I have one mailsetup with opensmtpd where we do this because $contracts and $compliance and other $nonsense.
Its the same setup I wrote about in the opensmtpd blog, but the config ends with:
relay in this sense doesnt mean realy to a smtp server that actually sends the mail for you but kind of just "send it".
Trust me, its not what you want. You want a mailrelay. Click SMTP accounts, and set them up in postfix, or better opensmtpd, because then you wont have to study postfix (as in university study for half a year) to know what you are doing.
Dont set SPF records to your servers, you will regret it.