Local email server that connects to remote server

I know this is possible but I'm unsure whether there is a ready made solution or if this would be a custom coded (which most likely wouldn't get approved)

My company has it's email handled by a hosting company. We're looking at having a local server to act like a cache while letting us send email through the hosted email server


example:

hosted address: user@company.com
local address: user@company.local


the local server would download the emails off of the hosted server through POP3 and the user would connect to the local server through IMAP (this way no matter what workstation they use their emails are there)
When sending an email the local server would almost act like a proxy and send the email through the hosted server using the user@company.com account (so we're not marked at spam as the reverse lookup would fail on the company.local)



The reasoning behind this is right now users are using POP3 so the emails are lost if they move workstations and if the hard drive fails they're hooped... Not only that but on rare occasions the internet goes down so we don't want to dish out the money for redundancy or lose access to our mail (which is why we don't rely on IMAP from the host or just host the email server ourselves)

Thanks!