It's a scam
Payroll companies do not ask strangers to send pay stubs. They are printed and mailed out directly from their office. It would be a security breach to ask a person to do this from home
And NO real company pays through Moneygram. It's always a scam
Tell them you are sorry but until you have interviewed at their office you cannot accept the position. And that you need them to issue you an I-9 before you can start, as required BY LAW
100% Scam.
You would be sending out fake checks. This is how the scammers distance themselves from their scam. They have some other sucker do their dirty work. When the scam unravels, and the police, FBI and postal inspectors get involved, guess whose house that they go to?
Yes this is a scam or some kind of illegal activity. Don't get involved. They might be using the name of a legit company, but they aren't
Moneygram is for sending money to relatives and friends, nothing else. Scammers always exploit wire services.