After many trials and errors, it finally worked (almost by chance). I am sharing the information here.
Say that your web site address is
http://mydomain.com, that you have a directory called mydirectory and a file called myfile.htm. Suppose that you have renamed your file into myfile.php and than you want to redirect all the traffic intended for
http://mydomain.com/myfile.html to
http://mydomain.com/mydirectory/myfile.php
First, I tried these directives and none of them worked:
Redirect 301 /mydomain.com/mydirectory/myfile.html
http://mydomain.com/mydirectory/myfile.php
and
Redirect 301 /www/mydomain.com/mydirectory/myfile.html
http://mydomain.com/mydirectory/myfile.php
Then, I started playing a bit with the params, trying to supply non-existing files and directories, to see how will the server behave (some sort of functional analysis as I did not really want to go through lengthy Apache tutorial pages). I finally typed in something like this and it worked like a charm:
Redirect 301 /mydirectory/myfile.html
http://mydomain.com/mydirectory/myfile.php
It was as simple as that and I am really glad that it works.
Also, thanks to the support team for their fast replies.