Oldhousehelp

Hi All, I have a problem with my kitchen flat roof which is leaking in a few places when there is heavy rain. The roof is felt, which is cracked along the outside edge and therefore letting in water. Some of the boards under the felt are damp and could be replaced. I am happy for a temporary fix as I will be putting the house on the market in the next few months. I have contacted two tradesmen looking for a repair job. One said he would torch on a length of felt down the front run of the roof where all the existing felt is perished, Also tidy up the upstand on the far side. Once felt is down, run a roof sealer over the edge for extra measures. The second said the damage is too great to repair and he would replace the whole roof with a 2 layer system of good felt and replace any damaged boards. I have attached some photos. I’m told there is a small hole close to the main back wall of the house, which is letting in water. I haven’t got a photo of this currently. Any advice regarding if the repair job quoted by the first tradesman would be enough to solve the problem temporarily. Or if that’s a waste of time/money and a new felt roof is required? Thank you!