The laser pump-probe technique is used to study the electron impact transfer between the 1s5 and 1s4 states of argon (in Paschen's notation) belonging to the 2P3/2 ion core for electron temperatures in the range of 1-2 eV. A rate coefficient of m3s-1 is determined for the transfer from 1s5 to 1s4 state. Different pumping schemes between the 1s and 2p states but also 3p states are used to verify the obtained value but also to probe the transfers with ion-core change toward the 2P1/2 ion-core. Our results show the presence of an important transfer channel between 1s2 and 1s4 states, and a rate coefficient of m3 s-1 is estimated for this transfer. The present results confirm that recent quantum mechanical calculations by Zatsarinny et al  underestimate significantly the cross sections for electron impact transfers between 1s states of argon.