44510-47051 compatible with Japanese spec prius?

First, please read this >>linked post<< to understand that the number you quoted is not the part number (P/N). Toyota is known to stamp a manufacturing number (or maybe an internal SKU number) on parts that is different from the catalogue P/N. It does not help that the format of both numbers is the same format – xxxxx-yyyyy.
Toyota/Lexus2014electronic parts catalog

The P/N for your JDM-sourced 2008 Gen 2 Prius is 44500-47130. The site I use (Toyota/Lexus Electronic Parts Catalog) to find P/Ns generally only lists the original part number and does not show any modified part numbers. Note also that the part for all other Toyota markets is 44500-47140. US parts sites say that 44500-47140 is superseded by P/N 44500-47141.

If you are physically looking at that part in your car and it has a label on it like the one shown in the linked post, then you might be confident to assume the part you have will be the same as another you might find online that has that same number. However, you also might wonder why Toyota uses one P/N for the Japanese domestic market (44500-47130), and a different one for other markets (44500-47140).