Queenless

I discovered two weeks ago that one of my hives is without a queen.  I figured something was wrong with this hive when activity outside the hive dwindled.  Having two hives is really the best way for a new beekeeper to learn about such things.  Upon inspection in the hive, I found very few eggs and larvae but a lot of drones.  Seeing the eggs and larvae should be a good sign, but in actuality, it meant doom.  Why?  The sign of drones indicates a "false queen" is present in the hive.  A false queen is a worker bee laying unfertilized eggs which are drones.  Drones are male bees and males don't do much for a colony other than mate with the queen and gorge on honey.  Sorry y'all, but the male bees are loafers who eat honey and have the privilege of going to other hives and stealing their honey.  If a worker bee (i.e. female bee) were to go to another hive, they would be pushed out by the guard bees and possibly killed.  But justice does exist because when a drone mates with a queen, their internal organs are pulled out of their body and they fall from the sky dead.  C'est la vie!

This a close-up of a drone honeybee.  Their bodies are much larger, especially their eyes!!

These are all worker bees nursing the brood (baby bees).  They are significantly smaller than the drones.  If you look closely, you can see the curled-up larvae in the cells. 

The problem with having a false queen, is that the colony carries on with life as usual until eventually the food is gone because there are not enough worker bees to gather nectar and the worker bees eventually die of old age (about 6 weeks).  This process can happen fairly quickly.  The weakened colony is also under threat of robbers from other hives who can easily steal their honey.

I have three options to reviving this hive and getting a queen.  I can either:
1. Buy a queen.
2. The bees can raise a new queen from fertilized eggs and/or larvae (this frame comes from another hive).
3. Introduce a swarm.

After spending almost $100 for this colony, I wasn't willing to invest more money, and I can't just wait around for a swarm, so I decided to take a frame of eggs and larvae from my other thriving hive and put it in the queenless hive.  Ironically the frame I chose also had a partial queen cell on it.  It was a partial queen cell and I was trying to convince myself that it was a drone cell (because drone cells are bigger than worker cells and are located on the edges of the frame---the same location for queen cells) I was in denial because I didn't want this colony to swarm (it's so robust and could potentially make a lot of excess honey!!).   All we can do is wait and see what happens because there's still a two week period before the queen emerges and mates and then another few weeks before the queen's eggs hatch.  Within that time period, the colony could dwindle and not survive because not enough bees would be around to take care of the nursery.  We'll see...

Question for you bee folks reading this:
If a "false queen" is present in the hive and a frame of eggs and larvae are introduced, will the workers even think to make a queen?  Meaning, will they even think they need a queen since there's a "false queen" laying??