Catalysis of the reaction: 1-(2-amino-2-deoxy-alpha-D-glucopyranoside)-1D-myo-inositol + L-cysteine + ATP = 1-D-myo-inosityl-2-L-cysteinylamido-2-deoxy-alpha-D-glucopyranoside + AMP + diphosphate + 2 H+. 1-(2-amino-2-deoxy-alpha-D-glucopyranoside)-1D-myo-inositol is also known as glucosaminyl-inositol or GlcN-Ins, and 1-D-myo-inosityl-2-L-cysteinylamido-2-deoxy-alpha-D-glucopyranoside as desacetylmycothiol or Cys-GlcN-Ins.