There is a ticking sound from the engine, loses power

It would be much better for your friend to create an account and create threads and add posts. When the information is going through a third person (you), things get lost in translation.

 

I'll guess clogged catalyst with a little of the exhaust being forced to escape elsewhere

...and that really is a guess, so don't give it much weight.

 

Why was it in the shop?

I agree, have your friend post here directly.

 

Which battery? The hybrid battery or the 12v battery.

 

To do that they would have disconnected the 12V battery. Car loses all its settings and all of its tuning information. May run a bit rough until it relearns. I'm not sure how long that takes, couple of hundred miles? Somebody else here will know.

That said, the "car loses power when you apply full power" isn't something I experienced after changing my car's HV pack. Nor were there any ticking noises.

Did your friend get a new battery or a rebuilt one? The latter, at least in the USA, are very hit and miss.

Since his problem seems to have become your problem, attach a competent scanner to his car and check for codes. Also check for the module voltages. The App "Dr. Prius" will provide a nice graphic of those voltages. Finally, open up the hood, get the car running, and see if you can localize where the ticking sound is coming from. It might not be the engine at all. The ABS makes noise, as do some of the pumps and valves. If you can hear the sound he is referring to make a short recording and post it here.