Basically, you cannot access another application's sandbox.
However, if you can modify the other application, you can use a ContentProvider or similar sharing solution to provide access to this specific file from other applications.
Store the shared file in a shared folder
As you want to access the file from different applications and the sandbox from one will not be available from the other, you should write your file in a directory accessible from both, for example:
String fileName = Environment.getExternalStorageDirectory().getPath() + "myFolderForBothApplications/myFileNameForBothApplications.txt";
Use a Content Provider
If you prefer to keep your file as part of one application, you can still expose the information via a ContentProvider.
In it, override the public ParcelFileDescriptor openFile(Uri uri, String mode)
method, and in the other application, just use the method getContentResolver().openInputStream(...)
.
And here a few links to related topics where I shamelessly copied/pasted code from: