I'll answer this in a little bit, ok sre?
Sorry sre, that was a little bit of a wait!
Ok- here we go- and if this is confusing, I apologize. It is a very complicated subject, and this is MOO.
If there is decomp scent on an item that has been able to retain scent for a long period of time, then an HRD dog should be able to hit on it after much time has passed. Items that retain decomp scent are very variable, and also very subject to environmental conditions. Also, the 'stage' of decomp matters as well- when the remains come into contact with various items.
So... this may be a thoroughly confusing analogy, but I'm gonna try it anyway.
Think about it like this:
As a test, you put an open can of tuna into your fridge, close the door and leave it closed for a week. There are tons of different foods in your fridge. Most will absorb the scent of tuna to varying degrees, depending on their packaging and their propensity for absorption. Take out that loaf of wonder bread that you left unwrapped? It's gonna smell like tuna. And it's gonna smell strongly like tuna if the can of tuna is right under it, on it, or next to it. The oranges though- not so much- because they have a strong scent of their own, and are sealed by their own peel.
Now you take out the can of tuna. Your fridge still smells like tuna. In the meantime, I have tried the same experiment with MY fridge- only I have a 2011 SubZero and you have a 1972 Fridgidaire. Does the food in my fridge retain scent longer than yours, because it keeps a more consistant and sealed temp? Or does the food in your fridge retain less scent, because it has dispersed into the environment (and you can now smell tuna on the other side of your house?) So I get hit with a huge scent of tuna when I open my fridge door...while you are sorta like "hmm, so that's what I've been smelling all week."
Now try the same experiment, only put your tuna in a ziplock bag. Or drop or raise the temp in your fridge. Or shut it off entirely. Or leave the door slightly ajar. The scent of tuna that permeates the other foods in your fridge will vary wildly. Do you see what I'm saying?
Decomp is the same for HRD dogs. The variables are tremendous.
So to answer your question of whether or not an HRD dog can alert to a site after a body has been moved...it depends on A LOT of variables.
Helpful, huh??