@Chris Neilsen provided the most practical and elegant solution to the problem (his code snippet follows):
Sheets("XYZ").Range("A2") = Sheets("XYZ").Range("A1").Value
In order to investigate and understand the possible cause of this strange behavior (may be a bug) of the Range object, I've posted couple comments, which are summarized below:
There is a conceptual difference between the original expression (see below):
Sheets("XYZ").Range("A2") = Sheets("XYZ").Range("A1")
and solution proposed by @Chris Neilsen, namely: original expression is implicitly assigning the Range object var (essentially, a pointer) to another Range object, like demonstrated in the following code snippet with explicit assignment:
Set rng = Sheets("XYZ").Range("A1")
Sheets("XYZ").Range("A2") = rng
while proposed solution explicitly passes the value property. Still, the reason why assigning a Range object failed for a value with string.Length>8202 is currently unclear (it may be caused by some internal nuances of the Excel Range object implementation).
Many thanks for posting this interesting question and fruitful discussion.
Regards,