Is it possible to reply or create emails to emails address on other domains?

Hi, I am trying to figure out a way so that I can have one Microsoft exchange email account setup in outlook with example domain123.com and have my google and hotmail email accounts forwarded to my domain123.com exchange account.  I already know how to setup forwarding from these hotmail and google mail accounts to this domain123.com account but what I don't know how to setup is how to reply to a hotmail or gmail account from outlook as the hotmail or gmail account and not the domain123.com exchange account so that the person I am replying to still thinks its coming back from the hotmail or gmail account.  I do not want to setup the hotmail or gmail accounts in outlook at all.  I just want the one exchange domain123.com account and have the ability to reply to any account or even create a new email from those accounts .  Is this possible?  Do i need special software to do this or is there a trick to setting this up.

Please let me know

Thank you