Well, you really had to pose a really hard question, didn't you?!
I think the only way you can do this, and this is only in theory, or maybe not so much theory but hard yakka (work, like in a real grind), which is to copy and past the data from one database format into another database format, i.e., from MS Access to SQLite. OK, with that said, when it comes to Pocket e-Sword resources, my understanding is (which I hope someone can validate this) that all Pocket e-Sword resources are HTML or CSS or something similar type files.
I hope this is helpful to you on which you can work with.
Sorry, didn't mean to cause your brain any pain! ;-) However, I find it hard to believe that no one else has asked the question. Although I've searched the Internet for the answer before, I have yet to find either where someone has asked or a solution was given.
I'm not as concerned about converting the resources as I am the user data. If the user data is indeed MS Access, do you need a licensed copy of the software in order to open and read it, or is there some other free software that can be used? Once it's determined what the user data format is, do I need to change the file extension in order to open it? If it ends up being a database file, will the database software be able to read it in such a way that I can parse through the records and visually read the record fields?
Although it may not be easy or straightforward as to how to do it, I believe it's going to be worth the effort. At the time, the Lord was giving me personal revelation and encouragement in the middle of many sleepless nights, and I'm at a place now where I need the reminders of what He had spoken and promised me!