You are defining the recurs_copy() function to perform the copy but you never execute it. Try:
function hyperbolic_activate() {
$src="https://wordpress.stackexchange.com/questions/112547/includes/myTheme/";
$dst="../themes/";
recurs_copy($src, $dst);
}
register_activation_hook( __FILE__, 'hyperbolic_activate' );
function recurs_copy($src,$dst) {
$dir = opendir($src);
@mkdir($dst);
while(false !== ( $file = readdir($dir)) ) {
if (( $file != '.' ) && ( $file != '..' )) {
if ( is_dir($src . "https://wordpress.stackexchange.com/" . $file) ) {
recurse_copy($src . "https://wordpress.stackexchange.com/" . $file,$dst . "https://wordpress.stackexchange.com/" . $file);
} else {
copy($src . "https://wordpress.stackexchange.com/" . $file,$dst . "https://wordpress.stackexchange.com/" . $file);
}
}
}
closedir($dir);
}