Using Softphone's Remotely

Hi! My office uses an Asterix PBX with Polycom handsets. We would like to implement a system where users can remote in to their PC’s from outside the office and make/receive calls through a softphone on the PC, through their deskphone’s number. In other words, if someone rings their extension, the softphone will ring and they can pick up. I have tested softphone’s (X-lite and Mizu) using Remote Desktop and web-based remote tools, but speech does not work, only audio.

Has someone implemented a similar solution?