When flying into headwinds of greater than 100 kts, TAS should be decreased in order to improve Ground NM per gallon.
Depends on current TAS!
IF you are currently at no-wind max range airspeed, then you increase airspeed in a headwind to increase range.
The limit will differ with airplanes, depending on where the "knee in the curve" of fuel flow vs IAS is.
For example, in the 744, you will seldom go above 0.86 IMN because fuel flow increases drastically above that, even though Mmo is 0.92.
A rule of thumb is to increase TAS by about 40-50% of headwind component. Again, YMMV between airplane types.