What I wish to do would be to include among my PHP scripts in short Press theme. However , once i range from the script file I can not access, inside functions within the theme file, variables declared within the script file .

I've produced a brand new file within the theme folder and added exactly the same code as with header.php and when I open that file it really works all right. So so far as I will tell it is something Word Press related.

/other/path/wordpress/wp-content/themes/theme-name/header.php // this is broken
/other/path/wordpress/wp-content/themes/theme-name/test.php   // this works

/var/www/vhosts/domain/wordpress/ ->(symlink)-> /other/path/wordpress/
                                                /other/path/wordpress/wp-content/themes/theme-name/header.php
/var/www/vhosts/domain/include_file.php

Content of: /var/www/vhosts/domain/include_file.php

$global_var = 'global';
print_r($GLOBALS);  // if I open this file directly this prints globals WITH $global_var;
                    // if this file is included in header this prints all the WP stuff WITHOUT $global_var;

Content of: /other/path/wordpress/wordpress-content/styles/theme-title/header.php require '/path/to/include_file.php'

print $global_var; // this prints 'global' as expected
function test()
{
    global $global_var;
    print $global_var; // this is NULL
}
test();
print_r($GLOBALS); // this prints all the WP stuff WITHOUT $global_var in it

I am not marketing using $GLOBALS, but anyway... define your variable using:

$GLOBALS['varname'] = 'value';

That will work. I suspect you are not really in global scope as if you think you're. That file is most likely being include with a function, by which situation you are in function-scope.