This relay isn't allowed to send mail "From" me.com

We have a domain on a Virtual Private Server hosted in GoDaddy and I have set up an email that forwards to a me.com email, the email gets delivered to the me.com email but when I respond from there I get a (This relay isn't allowed to send mail "From" me.com) delivery failure message.

How can I set up any arbitrary Mail client to send as me?

Apple doesn’t allow other Mail servers to send Mail on their behalf for security reasons - only authenticated Mail clients can send. Since your VPS isn’t an Apple server, no one will accept your reply as if you were Apple sending that reply.

• https://support.apple.com/guide/icloud/what-is-icloud-mail-mm6b1a17e3/icloud

Are you able to set up your me.com account on your Mail clients or use webmail with iCloud in the VPS?