Ok I have an answer for you!
First of all what you are asking is certainly possible.
It is called:
Off-site CCTV Recording.
Some companies offer a cheaper version. Some offer a proper Dedicated Secure Remote CCTV recording.
These guys offer remote recording and they setup the full system >
http://QRcctv.co.uk
Not all DVRs are compatible for this. (Cheap DVRs can never ever perform this function 24/7. (They may be able to handle a few hours at a time.
I would not recommend a screen recording software! Imagine what a pain it is to search for footage, the resolution you lose....etc.