Please I need a routine with which I can read and write to a known file in a remote computer on the internet.

That is a very dangerous thing to do: think about it: in order to read and write file file across the internet, you have to give generic access permission to everybody. Which means that whatever your file contains, it had better be irrelevant and unnecessary, because someone, somewhere, is going to screw it up, just for fun.

Think about what you are trying to do, and consider using a database instead (these can be secured reasonably well) or if necessary consider creating a web service to do the reading and writing. This can be as secure as you need it to be.