My dad uses MS Outlook on a laptop and a desktop. As you may or may not know, Outlook stores all it's data in a PST file, which you can store wherever you want. He wants his laptop and desktop to "share" the same PST file. He would prefer it if the PST file was stored on the desktop, and if he could access it on his laptop wherever he is, as long as he's got an internet connection.
No, that's not something you can do with Outlook. I know, I've tried.
You can put it to a common network connection so that two machines can access it at the same time, but if one has it open and the other tries to open it, it messes up the whole configuration due to file locks.
On top of that, PST files cannot be made available offline, meaning the laptop would have to be connected to the local network if it were to open Outlook. If you open it when it doesn't have access to the PST file, it messes up the whole configuration and you'll have to redo it. It's ugly.
And finally, network performance on PST files is horrible. It causes multiple errors and latency problems every time you work with it.
It's better to configure Outlook to not remove the mail messages from the mail server when it picks up the mail, but only remove it if it is deleted locally first. This would allow (mostly) the same mail content for both computers. There will be some issues with mail on one machine and not on another, mostly from deleted items that were deleted on one but didn't replicate to the other.
This is the main reason that web client mail became popular. I highly recommend it over Outlook. Outlook is mainly intended for Exchange server in a corporate environment, and lacks a lot of features for working with other mail servers.
Dgingeri is correct on this. Messing with Outlook gets really messy. I've got several clients that use Outlook currently, and are wanting to do more and more sharing or remote access. The solution has always been get away from Outlook. Webmail clients of many different types are available for free, often with many of the same features and layout as you might be familiar with from Outlook, but you don't have the hassle of local hosting, data backup, corrupt database files, etc.
I'd recommend you look into Outlook.com I've really been impressed so far with the very simplistic usage yet very powerful toolset you can have all from your web browser. I've got an account set up on there, and you can have multiple other email accounts also linked and accessible all from one place. If you're going to be needing to access your email remotely or from multiple sources, webmail clients like Gmail or Outlook.com are going to be your way to go.
You can do what you want with Outlook, but you would have to configure each PC, the desktop and the laptop, to store their e-mail files in a PST file local to each computer, so that each computer would have its own PST file. Then you configure Outlook to only delete e-mails from the server after 45 days. Any server should be able to store 45 days worth of e-mails, unless he sends and receives a TON of e-mails.
By not deleting e-mails from the server for 30 or 45 days it allows each client, the laptop and desktop, to synchronize their PST files with whatever's on the server. For instance, an e-mail he sends from Outlook on his laptop gets copied to the server's Sent folder. A couple of days later, when he logs into his e-mail account with Outlook on his desktop, all e-mail folders on the server will be synced with the PST folders on his desktop. Any e-mails sent or received since the last time his desktop logged on with Outlook will be copied to his desktop PST file. Same with his laptop PST file next time he logs on to his e-mail from that PC.