A memorial of a document means a summary of it. The document doesn't have to be a will, it could be, for example, a deed. Presumably, a memorial of this will was made as part of the process of obtaining probate.
Wakefield was in the West Riding of Yorkshire and the Archdeaconry of York. I would guess that some of the property lay in the Archdeaconry of York (or perhaps another Yorkshire jurisdiction), which would have fallen outside the Chester jurisdiction, and that may explain the Wakefield involvement.
Presumably, Book A3 page 637 and Number 771 is a reference to the memorial in the register book.
There are various reasons why the probate may have taken so long, but it is hard to say from the information provided.
Perhaps another Rootschatter can help further.