If you copy the old Sticky Notes.snt to:
%LOCALAPPDATA%\Packages\Microsoft.MicrosoftStickyNotes_8wekyb3d8bbw\LocalState\Legacy\ThresholdNotes.snt
They should be upgraded when you reboot the new Sticky Notes app.
Reference
https://www.reddit.com/r/Windows10/comments/4wxfds/transfermigrate_sticky_notes_to_new_anniversary/