My taps are similar and can be taken apart as follows.
1. remove the screw as you have already done.
2. point the tap directly towards you and then move it 90 degrees away from you (it could be either way so try it both ways)
3. Pull the tap upwards and it should slide off.
Fitting is just a reversal of the above.
I hope this works for you but cannot guarantee you have the same tap as me. Let us know how you get on.
Alan
January 2005