Not sure what you mean by
" like emails, modify the content like
[original nubmer]send you a message: [message details]"

as for email forwarding, I only have the option to set the subject on the router GUI, which is added in front of the subject that the forwarder has by default.

like this:

Subject: Test

Emali subject Test received a message from [original sender number / name]

So, if you can point me in the right direction where I can find more information about SMS forwarding customization it will much appreciated.

Thank you.