Product A and B can be distinguished by

(A) is primary amine, so it gives carbylamine reaction with  ${\text{CHCl}}_{\text{3}}\text{, }\overline{\text{O}}\text{H}$ form soluble sulphonamide with p-toluene sulphonyl chloride, liberates $N_2$ to give alcohol with $HN{O}_2$, (A) also gives smell of mustard oil when treated with $C{S}_2/HgC{l}_2$
(B) is a secondary amine, so it does not give carbylamine (or) mustard oil reaction. Further it forms oily nitrosamine p-toluene sulphonyl chloride