Your question seems to have been added twice. There are replies to your earlier query.

Oh dear. Never mind, these things happen.

It is not a problem

The answer is yes providing they are not protected files a good program to use is Calibre free to download when you have the program running plug your Kindle in and an icon of your Kindle will appear you can then drag a book from Calibre to your Kindle you have to drag the book to Calibre first.
Another way is to email an attached book to your Kindle email address this can be found in your Kindle settings this would look something like steragram@kindle .com depending what you have used for your Kindle.
The only other thing you have to make sure is the book is the right format mobi
You can change the format with Calibre hope this doesn’t sound to complicated it isn’t.

I don't have a Kindle Peter, just the dowloaded Kindle app - not sure if that would work the same way>

Yes you would still have a unique kindle email address if you look in settings
You can email a book to it the only thing is you may have to go to your Amazon account and authorise the email account you are sending the book from to be able to do it.
You only have to do this once.
I often share books this way and the books just appear on their Kindle or in their app.