Since @biogirl has given an answer, I'll add my opinion:
β-galactosidase would be expressed but the permease and transacetylase would not.
The operator lies adjacent to/slightly overlaps the promoter, upstream of the lacZ gene. Binding of the repressor to the operator blocks the promoter, and induction of theoperon involves the repressor leaving the operator unoccupied. If you precisely excised the operator and transplanted it between the lacZ and lacY genes then I think the promoter would be constitutively expressed leading to β-galactosidase synthesis, but the operator would block the polymerase from transcribing the permease gene. In this view the operator would be acting more like a terminator.
Then, if an inducer was added it would relieve the effect of the transplanted operator and the downstream genes would be transcribed. It's even possible that this experiment has been done sometime in the last three decades.
The OP has now edited the question in such a way as to make my answer, and the answer from @biogirl, nonsensical. The original wording referred to moving "the lac operon" not "the lac promoter", hence my question in a comment asking "operon" or "operator"?
I'll leave my answer here, but this question is now so compromised that I advise everyone to just forget about it.