How does the CFM LEAP-1B engine achieve the same efficiency as the LEAP-1A despite its lower bypass ratio?
Bypass ratio (BPR) alone never tells the whole story.

Take a low BPR engine and add to it a bigger fan, now you have higher BPR. Does that mean better efficiency? No. The reason is simple, by keeping everything the same, the same combustor/turbine do not have the right power/design to turn the now bigger fan at the optimum speed (slow fan).

But if you use a smaller fan on an already high BPR engine, which is the -1B case (approx. 8 inches smaller), then the thrust will be lower, which is indeed the case (approx. 130 vs. 143 kN). Since the combustor and OPR (overall pressure ratio) haven't changed, they can easily drive the now smaller fan at the right speed.

The other benefits the -1B have that may offset the lower BPR are the lighter weight (2 fewer turbine stages), lower duct loses, and the Max's cruise Mach, which is 0.01 faster than the neo – the slightly faster speed means slightly less time burning fuel for the same distance, and also slightly better inlet compression.

The LEAP SFC values aren't public yet. The official statement is:


  The advanced LEAP engine provides a 15 percent improvement in specific fuel consumption (SFC) compared to today's CFM56 engines.


That can also mean compared to the CFM56 of the respective plane, which is different for the A320ceo and 737NG:


  CFM56-5A1
  A320-211/-311
  0.330 lb/lbf hr
  
  CFM56-7B24
  737-700/-800/-900, 737-700BBJ/-800BBJ2 (option)
  0.370 lb/lbf hr


Source: jet-engine.net



The main reason there has been an increase in BPR in recent times, is because of the higher OPR they've been able to design (powerful small cores). Without OPR, you can't drive big fans at the right speed using small cores.

The slide below by Safran also shows why BPR alone is not the full picture:


(Safran via forum-ae.eu)



Related: Why does the CF6 have a lower bypass ratio than the TF39?