Are you sure she didn't say six weeks?
I checked both the OPM and U.S. Postal Service webpages. At 15 years' service, the leave accrual rate goes to eight hours per pay period, or 26 days a year. (Very generous.) Add 13 sick days.
I suppose one could add the 10 federal holidays, but we're still well short of 16 weeks. I don't know what the carryover maximum is. The Post Office may allow large carryovers, which (as you know) people tend to fold into their retirement planning.
It's a very generous leave system any way you slice it, but I don't know how this person could get to 16 weeks in regular annual leave. Unless she works for the French or German postal services, which is a different thing.
I had a golfing friend who worked as a mailman for twenty years and retired. He had accumulated a lot of sick time, was given credit for all of it and paid for it. His retirement pay was excellent, better than mine and I did 36 years in a big company. Gummint pay is pretty good but their retirement pay is terrific. The new postal rates are due anytime now. Someone has to pay for their hard work.