I'm not exactly sure how you plan on interfacing the mobile phone with the computer/pbx.
If you can get the mobile phone to use a standard phone line connection like RJ11, you can use a Linksys FXO adapter
.
This will hook up your existing phone line connected to the adapter and convert it to a voip line, so any phone or softphone in the office connected to the Axon pbx system can make and take phone calls from the GSM/mobile phone line. However, it is important to note that the FXO adapter only supports 1 line.
Also If you are just looking at a simple way of making free calls between offices, I recommend either
1) You have the remote office softphones connect to the central office Axon pbx system so all phones go through the same system regardless of office location, and then simply phoning the designated extension of the person you want to call
2) Use a free SIP service that allows you to call SIP numbers for free and simply have each office connect to one of these SIP accounts as an external line so calls can be made to any of the locations free.