i have one letter wrong on my green card

[hany99m]

hi all
i have 1 letter wrong in my green card it is in middel name
i go INS i fix my name in system. and they told me send ur card they will fix it free.. but it take a year!!! i don't know it wright or wrong ?? and i need my card fix i have jop they need my name fix ..

my Question is
if i said i lost my card and i will pay fee .. is will be faster or the same??

plz advice....