How to estimate mRNA counts from Relative Promoter Units (RPU) or RNAP per second (PoPS) in E. coli?
I could not find any paper that discusses these issues. So this answer is just based on my guess.

From the this page: 


  Transcription rate is generally a parameter associated with a
  particular transcript and has units of transcripts per unit time. In
  contrast, PoPS is essentially transcription rate at a particular
  location on the DNA. The value of PoPS just downstream of a coding
  region should be equal to the coding region's transcription rate.
  However, there are certain positions at which a transcription rate
  doesn't necessarily make sense yet PoPS does. For instance, as
  biological engineers, we care about the rate at which RNA polymerase
  moves through a terminator (or the PoPS downstream of a terminator)
  but yet most people don't talk about the transcription rate of a
  terminator.


What we want is the transcription rate for every gene. You can estimate it using PoPS corresponding to that terminator. 

Now, at steady state the mRNA concentration would be the rate of formation divided by the rate of degradation (removal): rf / rd.

Since the study that you are referring to, calculates PoPs, I would guess that it is based on some standard BioBricks parts. You are likely to have have mRNA degradation rates associated with these transcripts (even protein formation and degradation rates, possibly). If you don't have the mRNA degradation rate then at least for long lived mRNAs, you can assume the rate of removal to be same as the dilution rate (loge2 / doubling time). Substitute this in the equation for steady state and you should get mRNA concentration.

Steady state protein counts would be: mRNA counts × protein formation rate / protein removal rate.