How do I add php to all links automatically?

Inserting PHP is not really the way you want to do this. You would then need additional code to execute the PHP in the post body. It could be complicated.

1. Replace the links using a filter on the_content. Something like this:

   function replace_urls_wpse_91463($matches) {
     $ret="<a";
     if (isset($matches[1])) {
       $ret .= $matches[1];
     } 
     if (isset($matches[2])) {
       $home = parse_url(get_home_url());
       $url = parse_url($matches[2]);
       if (isset($url['host']) && $home['host'] !== $url['host']) {
         $link = $matches[2];
       } 
       if (!isset($url['host']) && isset($url['path'])) {
         $link = get_home_url('',$url['path']);
       } 
       $ret .= 'href="'.$link.'"';
     }
     if (isset($matches[3])) {
       $ret .= $matches[3];
     } 
     $ret .= '>';
     if (isset($matches[4])) {
       $ret .= $matches[4];
     } 
     $ret .= '</a>';
     return $ret;
   }
   function replace_urls_filter_wpse_91463($content){
     $content = preg_replace_callback('/<a([^>]*)href=(?:"|\')([^"\']*)(?:"|\')([^>]*)>([^<]*)/','replace_urls_wpse_91463',$content);
     return $content;
   }
   add_filter('the_content','replace_urls_filter_wpse_91463',1000);
   

   And I stress something like that, because that was put together in a hurry and will probably break in all kinds of horrible ways. And besides, parsing HTML with regex is pretty dicey even on a good day. Fun? Yes. Reliable? Not so much. I would recommend option #2. I am sure that could be cleaned up– a lot– but again, I would recommend option #2

2. Create a shortcode. Your people enter [url link="https://wordpress.stackexchange.com/london"]London[/url]. Something like this:

   function makeurl_sc_wpse_91463($atts,$content) {
       extract(shortcode_atts(array(),$atts));
       $home = parse_url(get_home_url());
   
       if (!isset($atts['link'])) return;
       $link = parse_url($atts['link']);
   
       if (isset($link['host']) && $link['host'] !== $home['host']) {
         $link = $atts['link'];
       } elseif (isset($link['path'])) {
         $link = get_home_url('',$link['path']);
       }
   
       $pat="<a href="https://wordpress.stackexchange.com/questions/91463/%s">%s</a>";
     return sprintf($pat,$link,$content);
   }
   add_shortcode('url', 'makeurl_sc_wpse_91463');
   

   Much nicer, and likely far more reliable. As before, this was put together in a hurry but it does have the minimal functionality mentioned in your question. I wouldn’t put it into production without thorough testing and debugging.