Adding mod to the existing game where tech is already researched does not register PUM to the player' crafting menu.

Are you sure, because I definitely checked this case and it works for me? Without other modded entities, it's right between the constant combinator and the power switch in the crafting menu. If it's really not there, can you share a save or at least the list of your other mods so I can look for weird interactions?

Yep, I'm sure. Re-researching with conole adds the item. Otherwise it's not there.

My mod list (quite long; maybe Circuit_Power_Measurement_Combinator or Inventory Sensor is the one causing problem?):
aai-signal-transmission
aai-vehicles-flame-tank
aai-vehicles-laser-tank
aai-vehicles-miner
aai-vehicles-warden
accumulator-wagon
alien-biomes
alien-biomes-hr-terrain
Armored-train
Armor_pockets
artillery-bombardment-remote
AtomicArtillery
auto_manual_mode
Circuit_Power_Measurement_Combinator
Dectorio
DiscoScience
DoubleFurnace
DragonIndustries
even-distribution
FARL
fireproof-trains
flamethrower-fluid
Flare Stack
Geothermal
Hovercrafts
InlaidLampsExtended
Inventory Sensor
LJD_Vehicles_A16
logistic-cargo-wagon
LogisticTrainNetwork
LTN_Combinator
LTN_Tracker
MaxRateCalculator
MIRV
module-requestor
MushroomCloud
MustardArtilleryShell
NapalmArtillery
NextGenEvolution
nicefill
OpteraLib
Orbital Ion Cannon
PavementDriveAssist
pollution-detector
PowerPlusPowerMeter
quickbarimportexport
Raven
Renamer
Robocharger
SantasNixieTubeDisplay
ScanningRadar
SchallCombatRobotics
SchallTransportGroup
Shortcuts
smallNightvision
SolarWalls
Soundpack-alerts-and-sirens
Space_Pack_200
stdlib
StorageTank2
SupplyToggle
textplates
train-station-overview
traincolorsignal
UraniumBelts
VehicleSnap
VehicleWagon2
vtk-cannon-turret
WireShortcuts

I've checked with Circuit_Power_Measurement_Combinator and Inventory Sensor and by themselves they didn't seem to cause an issue. I've released a new version where I added a migration that attempts to "force" the unlock, if the save qualifies, please update (0.1.3) and check. If it doesn't help, then I think I would need a save to sync all those mods. If you don't want to share your actual save, please make a "clean" save with the issue reproduced (so start a new game with all your mods sans this mod, console research "circuit-network", add this mod, check if the issue exists, and give me that save).

Update fixed the problem.
Thank you.