Cavity Block wall abutment to solid stone wall question

[RobertG]

Hi, 

My builder has just used cement to fill the join between the two walls. The cavity block wall and the stone, rubble and lime mortar wall. I can see the damp penetrating the blockwork but the lime mortar wall dries well as it should. 
 

Can someone advise what I should expect for this area of the construction? I can’t see this as being acceptable. Photo provided.