The plugin uses database table and for database prefix it gets the default wordpress prefix.
As a result, it only works with the main site.
A simple code edit will make it work on 'one' of the child site (not all). But it's not a very good practice.
1. find out the database prefix for your target child site
2. use that prefix to edit the code of the file 'srizon-fb-db.php' as follows
replace all of the following code with your database prefix
for example if you find a line like following and your db prefix for the child site is 'ch1_'
$table = $wpdb->prefix.'srzfb_galleries';
then change it to
$table = 'ch1_'.'srzfb_galleries';
after making all the changes, save the file and deactivate+activate the plugin.
This is just an workaround until I make the plugin multi site supported.