There's no need for more capital to buy shares. As the sold option goes ITM, go deeper ITM, and buy the option 3-4 strikes below at about 80 delta or so.
Sort of a double down on a position going bad? I think you might just lock in a loss doint that. It will cost more than the sell call itm value, why don't just buy the short back and reduce risk exposure?
for his own reasons, he wants to buy shares and continue holding the position. I suggested an alternative to buying shares.