So you cloned a site to another instance on the same server by a different FQDN.
That means separate DB, separate data directory, separate code directory.
They can't both be using the same FQDN so you must have had to do a config file for the cloned site in virtual apache configurations ... and maybe other configs for php-fmp or whatever.
The original site ... the one you cloned from, still works.
It's the cloned site running under a different FQDN on same server that's semi messed up ... any 'admin' link will not work.
Mind sharing what the file system looks like with focus on the two instances of Moodle?
Example:
FQDN1 - the moodle instance you cloned.
code: /var/www/html/
data: /var/www/moodledata
DB server: localhost
DB: fqdn1moodle
FQDN2 - the clone
code: /home/clone/html/
data: /home/clone/moodledata
DB server: localhost
DB: fqdn2moodle
Nothing is shared between them ...
DB server might be on localhost but the DB's are different.
In order for that to work there must be virtual apache configs for the virtual sites.
What do those look like?
Also ... any .htaccess files .... in any code directory? When you tar balled the code directory of FQDN1 and it had an .htaccess file that same .htaccess file is in FQDN2. Anything in the cloned .htaccess file that might cause this?
Any rewrite rules set for default virtual apache server?
Don't think that disclosing what operating system running is a security concern ... if anything, best to share with 'white hats' rather than let 'black hats' help you discover stuff.
Uhhh ... Emma and I do wear white hats! ;)
'spirit of sharing', Ken