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A1579345A in search field and search by
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A1579345A
LITHIUM ION BATTERY ASSY
Currently In Stock: No
Unit Price (in USD):$76.15
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(There seems to be none in stock to order but they must be available somewhere.)
Not much help I'm afraid except I've found the original part number. I'm not sure if anyone makes knock-off batteries at a cheaper price. I'm not sure if the batteries are interchangeable between models.
I would call a Sony repair depot and ask if they can supply a battery.
*edit*
A search found
one other supplier of part A1579345A. Their site says they will ship within, and almost anywhere outside, the US. I do not know the reputation/reliability of this company.