I appreciate this post is a little bit out of date for the poster, but I would have appreciated the following information:
After having a dig round I found the notes you make are saved to the file:
[SD CARD]:\Android\data\org.lds.ldssa\files\gospel-library\CONTENT_LIBRARY
(Note: this is only if you have put the Gospel library app to your SD card)
I copied this file to my computer then opened it with a text editor and searched for a line I had put in to the notes and hey presto there are all there!
... however it is not very readable. The file heading says the file is in sqlite format 3 so I downloaded Sqlite3Explorer from:
http://www.singular.gr/sqlite
downloaded
http://www.sqlite.org/sqlite-dll-win32-x86-3070800.zip (as shown on
http://www.sqlite.org/download.html)
and put the sqlite.dll in my c:\windows\system32 directory (so it would be in my path - if I could have been bothered I could have put in a different folder and added that folder to my windows path)
I then opened the Sqlite3Explorer.exe (which will not work without the .dll) and opened the CONTENT_LIBRARY file. There is a folder called notes, if you right click on it and click 'show data' then your notes are displayed as rows in the sqlite database.
If you are still not happy you can, in Sqlite3Explorer with these results showing, click on 'file' and click on 'Save Result set as XML'.
I now have all my notes on my desktop in XML format to do with as I see fit.
If only they add a community to allow your notes to be shared and read other people's shared notes, and if only they would give a bit more flexibility about how you write notes/highlight (for a line, chapter, set of chapters - all of king Benjamin's speech for example or book). There are some interesting times coming... : )
p.s. I know you are all doing it for free, and if I ever get time I might sign up to add it myself! :p
edit: in terms of actually answering the question I imagine just copy the CONTENT_LIBRARY file from your old phone SD card onto your new phone SD card will do the trick. I am a lot happier knowing I have that file as a backup in case anything goes wrong with my SD card.
Even easier for you: just take the old phones SD card and put it in the new phone?!?!