If you use cysteine hydrochloride monohydrate instead the anhydrous product, you have to take into account the higher Mw (+18 Da) and multiply the amount given in the recipe by 1.146, i. e. 0.1146 g/l instead of 0.1 g/l in your case. I doubt that it would make much of a difference for a growth medium, but it will allow you to be accurate when you quote the reference in future publications.

Following upon Pierre Béguin 's response, the L stands for Levorotatory [as opposed to D for Dextrorotatory] which comes from Fisher projections of the 2 dimensional projection of the 3 dimensional amino acid structure for chiral compounds. This is analogous, but not identical, to the R and S nomenclature, which can differ because the method for determining R vs S differs from determining L vs D.

All amino acids that are incorporated into proteins are the L enantiomer, not the D.

Just to simplify the above answers. All amino acids come in D and L forms, which is explained nicely by Gary Lee Gilmore . So if this is being used as an amino acid for biological purposes, then you need the L form. There is no functional difference between whether you are making your solution from the anhydrous or monohydrate stock except you have to adjust for the correct formula weight. Note that they might have different solubilities though.