Sport Pilot – training in a certificated aircraft

Hi all - pretty sure I know the answer, I've tried to read through https://www.law.cornell.edu/cfr/text/14/part-61/subpart-J  fairly carefully, but I don't really deal with a lot of sport pilots.. 

Is it the case that I could provide training to a sport pilot candidate in a certificated aircraft not meeting LSA specs?  I know that they would eventually need to gain access and training in the LSA which they intend to fly, but is it fair to say if they choose to pursue some training in the certificated airplane, that those hours would "count" toward their Sport Pilot certificate?  I didn't see anything to the contrary anyway (though I have explained to him it may be more expensive, but hey....)

thanks!

adam

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