hi everyone
sorry if this is too basic. but i'm just not 100% sure. it is cheaper to buy united flight (sfo to frankfurt) from lufthansa. BUT united operates the flight NOT lufthansa. if i go ahead and buy the ticket (through lufthansa) i will still be able to upgrade to first using my free upgrades (or miles) through united mileage plus, right?

sorry if this is too basic. i've seen a lot about using mileageplus to upgrade on lufthansa operated flights but never this particular question (buy united through lufthansa, upgrade using mileageplus)

thanks in advance for your patience
hh