Unit conversion of Molar Conductivity
Refer to page 77 of Chemistry NCERT text book, class 12, part 1.  

You were actually right about the $\mathrm{10^4\ S\ cm^2/mol =S\ m^2 /mol}$. Check if the $\mathrm{10^3}$ you are referring to has molarity included in its equation because molarity is given as moles per litre.  

You can refer to the online NCERT book at its official website. Thank you, I hope this was useful and sorry if I got it wrong.