To estimate how difficult this will be you need primarily to know:

1. what os where they running on. What will it run on in house?

2. How much JNI is there?

3. What 3rd party packages does it rely on.  Do these run on your
in-house machine.

4. Are you going to change databases?

5. What documentation is there on how to run the system, and over all
docs on what it does.  Detail is rarely a problem. What you want to
check out is the docs at the head of each class and overall project
docs, and docs about what you have to run in what order for the daily
schedule.

6. What are the big problems with the code that will have to be fixed.

7. What improvements would they suggest (which is different from what
your users may be requesting).