Sticky Notes are handled differently in Windows 10 (to Win7 for example) so you cannot simply copy the file into the same location in the user profile and expect it to work. Assuming you have the .snt file from the Win7 PC, on the new Win 10 system run through the following steps:
1. Ensure no StickyNotes are open.
2. Go to Settings | System | Apps & Features | Sticky Notes | Advanced Options | Reset. [Note all existing app data, i.e. Win 10 Sticky Notes, will be deleted].
3. Navigate to: %LOCALAPPDATA%\Packages\Microsoft.MicrosoftStickyNotes_8wekyb3d8bbwe\LocalState
4. Create a New Folder within LocalState called Legacy
5. Copy the Notes.snt to the Legacy folder and rename it ThresholdNotes.snt
6. Launch Sticky Notes.