Failed to transfer saved ebooks in ADE between PCs (with the same Adobe ID)

I don't think the Adobe infrastructure will ever automatically copy ebooks between devices registered with the same ID.

You need to do the copying yourself explicitly.

Accessing a DRM eBook is a two step process.

1. Download .acsm file from whatever source (vendor, library, ...).  That is just a metadata file about the book and the purchase/loan.
2. Download DRM .epub file (or .pdf if you are unlucky).  Typically done with ADE.  The server will create a DRM file specific to the registered AdobeID.

You should then be able to copy the .epub file to another device (computer, dedicated eReader or tablet with eReader software) registered with the same AdobeID, and read the .epub there.

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I'm not sure if you can copy the .acsm file and redownload another DRM file for the same purchace or loan on a different machine.

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Usually copying is a standard process using a file manager such as Windows Explorer. 

The iPad infrastructure likes to make life hard for the user, so copying to an iPad has to be done indirectly: for example using Dropbox, iTunes or by emailing a file to yourself.