I have just upgraded from JMS MultiSites 1.2 to 1.3.16 on a Joomla! site with Joomla! 2.5.14 installed.

Before I attempt to install the patches, I see this message:

"Error connecting to the server: failed to open stream: no suitable wrapper could be found"

It also says the following, which appears to be incorrect:

"Jms Multi Sites
Version : 1.3.16 - basic (Latest available: 1.2.97)
Patches definition version 1.3.13 (Latest available: 1.2.91)"

When I click Install, I get the following errors:

Unable to write entry
Error during installation of the file "includes/defines_multisites.php"
Copy failed
Copy failed
Error connecting to the server: failed to open stream: no suitable wrapper could be found

I verified that I do have write permission to includes/defines_multisites.php

Regards,
Eddie

The first error message
"Error connecting to the server: failed to open stream: no suitable wrapper could be found"

Means that your server can not download a file from internet.
Perhaps that you have that to download the geo-localisation file or the joomla "installation.zip" file that is used during the "check patches".
A potential reason is due to the fact that the server forbid to use "open URL".

If you want to restore the "/installation" directory, you can do it by the restore from the standard joomla.zip package.

Concerning the other message that still make reference to JMS 1.2 it seems effectivelly that the patches was not correctly installed (update) and probably due to the previous error.

The "unable to write entry" and "copy failed" are generally due to permission that forbid to update file or create file.

To know exactly the file name or folder name, there is no other method than add a debugging trace in joomla. Joomla does not provide the possiblity to know the file name that cause the issue (even when the debug mode is enabled).