You guys are giving this person bad information here, or misinformation rather. He/she is using Samsung Notes, which is the same thing I have used for years on the various Samsung phones I have had. It is the standard Notes app that comes already installed on the phone stock, and you can use the widget to put on your homepage. Yes, it is the same app from phone to phone, and it is developed by Samsung Electronics, the actual Samsung company, and it is the "standard" notes app for Samsung.
Now having said that, I don't have an answer to your post OP. I've actually had issues where I had notes on a previous phone, without an SD card, that were security locked with fingerprint security, and upon trying to import with my Samsung account they were still locked and the password wouldn't work ( wouldn't allow me to just use my fingerprint with the new phone). So I guess that's in a way my answer to your question, if you used a "Samsung account" just like you would your email to back up your things on your phone such as contacts etc when buying a new phone, upon entering your account info on your new phone it would just import everything "Samsung" associated with it. If you didn't do that or an SD card, I don't think it will just import. I found this out because when I got the s8+ I did the normal act of logging on with email and importing everything with that, but Samsung Notes didn't import until I logged into my Samsung account, previously registered on a different phone.
Hope this helps, but just remember that if you "fingerprint lock them" for security, I would unlock them if you ever get a new phone to transfer them.