Webpage links not converting

Hello, hopefully someone can help me, I have created a web page with links to other pages, the trouble is that when I FTP it to my host, the links do not convert, and just stay as the old filenames.

How can I get the program to make the links work?

I used a FTP software years ago that was supplied by madasafish and that used to automatically convert the links for you.

Please help, as I am really stuck