As the old PB A is stated to be deceased since 2012, I presume you have one of the USB universal hard drive adapters to mount a bare drive.
What I would do is make a folder on the desktop of HD B and drag those apps and files you want to it. Then go through them to see which will work properly. If there are problems then search for and copy support files in the user library / Preferences and Application Support folders ( of course place them in the same folders on HD B).
If you want to manualy migrate existing Stickies notes from one computer to another you need to locate 3 files:
User/Library -> StickiesDatabase
User/Library/Preferences -> com.apple.Stickies.plist
User/Library/Preferences -> com.apple.Stickies.lockfile
You then need to ensure that they go into the same location on the 'target' computer