I didn't try it with a table, so this answer might be of very little value for you. But it works in normal text.

Make a bookmark for the original (select it, than Insert>Bookmark and give it a name). If you want a copy, Insert>Field>Links and references and choose Ref with the name of the bookmark as a parameter.

You need to refresh the field for the value to show up on the screen, I'm afraid. But it surely is printed.

There might be better tools to make fillable forms, such as Adobe Acrobat. I don't know of any free ones, but I don't exclude they exist.

Hope this helps.