I've been through the TRACES registration process - albeit for the purpose of importing organic products rather than animals.
Nonetheless my understanding is that the system interface is broadly the same, but the specific authorisations differ.
Despite being located in the EU (at least for another few months yet ) I have to say the process of getting set up and approved in the system seemed pretty confusing and opaque.
One of the problems we had was that some of the regulatory bodies didn't know what they were supposed to do within the system, so it gets to the point that we need the next part of the registration signed off by the FSA in the UK, and our local team have to use it so rarely that they aren't sure what they need to do...
Once it was clear to everyone what was supposed to happen it went relatively quickly, but getting to that stage was rather hard work.
The principle of the system is good; it should simplify some types of import, improve traceability and avoid the dreaded lost/delayed paperwork creating issues at customs. But getting to a point of sufficient familiarity to achieve this can be a bit of a headache, as the guidance docs aren't great. The Helpdesk service were also reasonably good (once they understood what we and/or the UK regulatory people didn't understand) so I'd definitely be suggesting to your client to contact them if they get stuck or confused.