I go with these guys and say yes. The straight Citation II is a two pilot aircraft. The fact that he chose to get a single pilot waiver only gives him a little more flexibility in it's operation, but he doesn't have to use the waiver. Here's something to think about: he's probably paying enough in additional insurance flying single pilot, that he could hire a co-pilot for the difference, hint, hint.

The Citation IISP is a little different story, in that it is certified single pilot right out the door and is equipped and weight limited for that reason, and any typed PIC can fly solo in it without a waiver. Still might be able to log SIC in one of them too, but I'm not sure of the in's and out's of that.

You will need a 61.55 checkout, which he, or any typed PIC can administer. Just look it up and see what it entails - basically a review of the systems, normal, abnormal, and emergency procedures, and minimum of three take-offs and landings. It's good for a year. Don't pencil-whip this. It's only to his and your benefit that this be given a fair amount of attention and is done properly.

You don't need an SIC type rating, unless planning to operate in a foreign country that requires both pilots to be typed.