App B does not have the rights to access files from App A. thats the primary point. It is not possible.
Store the Database on a Path accessible by both. Also note that you should NOT access the database from two apps at the same time. One app in foreground and the other app in background using a service or so. Sqlite is not able to handle this.
Or better; use a jRDC as Database middleware and access the data from both apps from this Database.
In Android you would need to create an ContentProvider in App A and Access this content from App B. But there is no Library to do so at this time i think. Or i do not remember having seen one.
In my wrap for the Whatsappstticker is a ContentProvider working. But it is one specific to some known files in the filesfolder (static files in this case).
If you are interested in reading more about it.
Creating a content Provider.