As far as I'm aware, this should work, as long as "spoofing" is allowed by the provider. Some providers do not allow you to change the outgoing caller ID to something other than the number(s) that you have been assigned by them. As I understand it, this can be a requirement by the regulators in certain countries.
It sounds as if you are receiving the caller ID, correctly from your provider. You might want to question your provider about the passing on, of numbers, other than your own.
When you call the mobile from your 3CX extension, I'm assuming that your SIP provider assigned number, is showing.