For other readers, please note that I-130 is NOT required for K1/K2 after US entry IF the I-129F couple marry within 90 days of arrival, as they promised to do. Again, no need to file I-130 if married within 90 days of US entry on K1.
After the couple's marriage and issuance of valid marriage certificate, K1 and K2 must file an I-485 package each, to apply for green cards. It doesn't matter who pays the filing fee. USCIS doesn't care whether the American or the intending immigrants pay, as long as the fee gets paid.