I've lived in Paranaque all my life, but never got the chance to visit the central post office. It's located on Sucat Road (going towards Duty Free), near SM Sucat after the overpass and sits by a curb (so it's easy to miss). If you reach the second overpass after SM Sucat it means you missed it already.
If you don't have a car you can ride any jeep or FX that passes through Sucat Road and just tell the driver that you're going down at the Post Office.
Here's a map that can help you find the Paranaque Central Post Office.
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