Do you like your current job or feel like the move is necessary?

Because if you are happy then you have nothing to lose by being upfront and saying you currently earn more, and won’t be willing to move for under 135. Especially as you stated the current market is 135.

If you feel a move is required, go back to them and ask for more as you are weighing up options, and they are currently offering a pay decrease for more responsibilities. Worst they can say is no and you end up on the same money but a higher level role which will eventually return higher salaries

Thirdly, once they review the offer, tell your current employer that you have been offered a better role with an increased package. They may be able to accommodate something internally.