"I invited them to provide the samples" is correct, but rather formal. Ok, if you want to be very polite or formal. Otherwise, I'd suggest using 'ask' ... "I asked them to provide the samples". "I invited them to provide the samples for." is incorrect. It is correct if you follow 'for' with what the samples are for. ie. 'test', 'experiment'. "I invited them to provide the samples for the experiment". As with #1, be aware 'invite' is somewhat formal. Ok if that is the intent or desire, otherwise use 'ask'.

The first one is correct: I invited them to provide the samples. The second one sounds strange for me. Though, if you want to emphasise that the samples were provided for them then you need to revise the sentence.

“1. I invited them to provide the samples.” fine, great? “2. I invited them to provide the samples for.” - no obvious meaning without something following the "for" I invited them to provide the samples for the experiment. I invited them to provide the samples for the assay. I invited them to provide the samples for analysis.

The reason why I asked this question is provide is usually used as the structure of provide something for somebody.