Ivomec, but you've got the dose too high. It's one-tenth ml (one-tenth cc) for a 5-10 pound LF and even less for a bantam. If you use pour-on it's two-tenths for a LF.
Injectable is fine; it's in propylene glycol and will spread around the skin pretty well. You can repeat the dose if you need to, every 10-14 days.
You can also use a 40:1 dilution of neem oil (your health food store likely has it) in water.
Now that he's there, unless your friend has practiced unbelievably strict quarantine the whole flock and the housing needs to be done. Everybody in the flock can have that dose of ivomec. For the housing, probably the gentlest thing is spinosad spray from your home center; it comes as a hose-end spray and should be used to wet down the entire coop and nesting areas until it gathers and runs off (in other words, get it wet, not just lightly misted). The great thing about spinosad is that it takes a couple hours to work so the mites carry it to each other. One wet mite can kill hundreds of hidden ones. That means it actually works better the worse the infestation is - and it keeps working for 14-21 days.