MSH acts as an oxidizing agent in this process, facilitating the conversion, which subsequently undergoes desulfurization. During this step, the intermediate undergoes a reaction where the benzyl group is eliminated from the molecule, and a double bond (C=C) forms between two adjacent carbon atoms. Hereafter the methyl ester is hydrolyzed.
Scheme 14 of this paper shows the mechanism: (Article ROSICS: Chemistry and proteomics of cysteine modifications i...
).
Thank you Robert Adolf Brinzer! The part that I'm actually still not sure about is the mechanism of the (first step) "Selective Amination" part which is unfortunately not given in this paper (or other papers).
If you read the original paper by Mukaiyama (https://www.thieme-connect.com/products/ejournals/pdf/10.1055/s-1977-24260.pdf) you will find it is an SN2 reaction where the sulphide is the nucleophile and the sulphonic acid is the leaving group.