Thanks to Ben Tasker

Assuming you’re running Postfix, it’s as simple as the steps below

First we make sure the virtual mappings file is enabled

vim /etc/postfix/main.cf

# Scroll down until you find virtual_alias_maps

# Make sure it reads something like
virtual_alias_maps = hash:/etc/postfix/virtual
# We also need to make sure the domain is enabled
virtual_alias_domains=example.com

Save and exit, next we add the aliases to our mapping file

nano /etc/postfix/virtual
# Forward mail for admin@example.com to jo.bloggs@hotmail.com
admin@example.com  jo.bloggs@hotmail.com

Simple! And if we want to send to two different addresses at once, we just specify them

admin@example.com  jo.bloggs@hotmail.com jos.wife@hotmail.com

Finally, we just need to create a hash (actually later versions of Postfix don’t require this)

postmap /etc/postfix/virtual

It’s exactly the same principle as passing mail into a local user’s mailbox.