Hello !
Just so you know, it's not really so feasable keeping them both. And I guess that with the costs you'd pay for this kind of cross update project, you'd rather get a second internet connection, you could pay it probably for some 2+ years with the same costs as this project.
However, if your boss really insists on it, then I'd like to learn some more details. So your offline people enter some data (eg. new order, products, customers - these are the main "entities" manipulated - into the offline system), while others do the same into the online system. So they need to sync to each other cross, that is two-way, which is very risky because IDs across the two systems won't match and even there are chances that different pieces of info become messed up (eg. some orders showing on different customers or wrong order numbers etc). There are ways to create a dual ID system, so that each new order to have an internal and an external ID, thus anyone would know where did the order come from. Same for new customers created. For the products I don't think this could be necessary, as I guess that only the local/internal people do the data entry for them, while those in the field only browse them in the online version.
It is a challenge, indeed, this whole project, so let's try to think more about the possible solutions, let's discuss them together online, here and see what the bottlenecks are and the possible other hazards to occur during the whole process.
Regards,
Dragos