It depends on what it does but if your customer is upgrading from 6 to 7 it's very likely it won't work anymore.
You will need to get hold of that source code and recompile it vs new major version. If it's an admin tool it will be pretty easy. If you customized something in edit mode it will likely take more time.
It shouldn't be too much work of you can get the source. Otherwise you will need to use dotPeek or similar to reverse engineer it. That will take a bit extra time as well...so ranging from a few days work to 5 to 8 work days of you need to reverse engineer it would be my best guess. (If it isn't a huge module)
Good luck :)
It also highly depends on what the module does, if it's related to any kind of URL rewriting, ex, then, it works completely differently.
Also, the API for content has changed in the meantime as well as new features, ex, blocks are added, so the functionality might not cover them. Same goes for files and Virtual Path Providers...
As Daniel suggested, without taking a peak at source code and understanding the functionality, you will not be able to answer the question. When you know what the functionality does, breaking changes might help you:
A former collegaue of mine created a module for episerver that interacts with our products. This module was created for EpiServer 6 i believe.
He has now left the company and our customers are asking if this module will work after they upgrade to newer versions of EpiServer.
I understand that you cannot give a specific answer regarding our module but has there been any major changes in how you develop theese things for epi in the later versions or would you say that it's likey that things that worked before should continue to do so?
I need to answer the customer rather quickly and do not have the time to set up an environment ant test each specific version. So any input would be greatly appreciated.