Catalysis of the reaction: 1-D-myo-inosityl-2-L-cysteinylamido-2-deoxy-alpha-D-glucopyranoside + acetyl-CoA = mycothiol + coenzyme A + H+. Mycothiol is also known as AcCys-GlcN-Ins and 1-D-myo-inosityl-2-L-cysteinylamido-2-deoxy-alpha-D-glucopyranoside as Cys-GlcN-Ins or desacetylmycothiol.