Mohammad

you can prepare this molecule, see

--- Preparation of organic mercapto compounds from organic halides and alkali metal or alkaline earth hydrosulfide

Kaji, Yuki et al,  Jpn. Kokai Tokkyo Koho, 2013018740, 31 Jan 2013

--- Synthesis and evaluation of a broad range of chiral sulfides for asymmetric sulfur ylide epoxidation of aldehydes

Aggarwal, Varinder K. et al,  Journal of the Chemical Society, Perkin Transactions 1, (20), 2604-2622; 2001

--- Cubane-Type Fe4S4 Clusters with Chiral Thiolate Ligation: Formation by Ligand Substitution, Detection of Intermediates by 1H NMR, and Solid State Structures Including Spontaneous Resolution Upon Crystallization

Lo, Wayne et al, Inorganic Chemistry, 50(21), 11082-11090; 2011

Good luck

If you're starting from glycerol, I would substitute one OH with Cl first.

To the mixture of  500 g of glycerol and glacial 10 g of acetic acid a gaseous hydrogen chloride is passed at 105-110° C until a weight increase of 190 g is achieved. Alternatively, gaseous hydrogen chloride is led into thoroughly dehydrated glycerol containing 2% of succinic acid for 8 h without heating, the heat of reaction alone causing the temperature to rise to 60-70° C. On distillation in a vacuum, mainly water passes over up to b.p. 114° C/14 mm, then between 114° C and 120° C 66 % or 360 g of 3-chloro-1,2-propanediol (b.p. 113.5710.5 mm).

Org. Syn., 2, 33 (1922).

Careful, the product is a known carcinogen.

Then you can do a simple substitution with NaSH, Na2S, thiourea, Lawesson's reagent, there are many procedures out there, altho I would avoid working with H2S given how toxic it is and the smell is unbearable.

If I need to do this, I will start from glycerol acetonide and convert the free hydroxyl group to thiol via mesylate or tosylate, following by deprotection.