I already told you third party claim. A lawyer could represent you against disability, and then bring in former attorney M to have him pay for whatever disability wants from you.
I don't know why S won't do that. Maybe your money amount is too little. Maybe you are a difficult client (suing former attorney is a sign) that he just don't want do the conflict of interest.
I told you everything I knew. The rest is up to you, get another lawyer if S doesn't give you want you want.