One of the ideas is to first upload the file in any of the free file sharing sites. Then post the link on the chatbox. But this seems to be very lengthy process. You may also have a lot of limitations with the file sharing sites.
A relatively easy method is by using Nimbuzz. You can either download the Nimbuzz messenger on your PC or use the web-based messenger. Nimbuzz also has the software for mobile phones. File-sharing works with all three. Firstly you need to create your Nimbuzz account. Then add your Facebook account. With this you can chat with your friend on Facebook via Nimbuzz. If you are chatting using Nimbuzz, there’s the send file option.
As soon as you click send file and select the file from your computer, Nimbuzz automatically uploads the file to its own server. The size-limit for file is 5MB. After uploading is completed, the link to file appears on Friend’s Chatbox with following message: