story identification - Distant aliens receive signal with instructions on how to construct humans, long after Earth is extinct

I'm looking for a specific scifi book that I read years ago, I only partially remember the story, and I don't remember the author or the title.

What I remember of the story is:

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  An alien race picks up a signal from humans that includes instructions on how to make their own humans (genetic instructions).

  
  


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  The humans grow up knowing they are created and are taught by the alien race.

  
  


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  They are eventually given resources to build a ship, and go looking for their origins.

  
  


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  They eventually find the solar system, but nobody answers.

  
  
  


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  They find some stations orbiting earth and find that the station is very old, so old in fact that humans have long been extinct and other creatures have reached local space, and have been looking around the station as an archeological dig.

  
  


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  I think they refer to two developed races from earth, but one developed from rats.

  
  

If anyone know what story this is, and can point me at it, its been driving me crazy for at least 15 years, and I think it's actually been much longer, since I can't remember when I read it.

Answer

This certainly sounds like The Genesis Quest by Donald Moffitt.

Though, I believe you have blended the story line from the second book (Second Genesis) into your description.

In the first book, the main characters are humans, raised by the aliens and their discovery that there are parts of the original message that were not fully understood by their alien friends and benefactors. As a result, the aliens give them the resources to build the ship.

In the second novel, the humans travel to source of the message. It is an ancient station (as you described) where they find that humans have become extinct, and the successor race on Earth had also gone extinct and a third species had evolved.