There's a lot that could be said on the topic, but to keep to the basics, the US doesn't have an inheritance tax but an estate tax, which taxes the estate of the decedent. Unless the estate of a US citizen or domiciliary (including all reported gifts up to the time of death) exceeds the current c.$12 million unified tax credit, there will be no federal tax on the estate no matter who inherits it.
Confusion seems to arise because the unified tax credit -- applicable to all US citizens and domiciliaries -- gets conflated with the unlimited marital deduction, which is available only to US-citizen spouses. My (totally unprofessional) understanding is that problems can arise when the value of the estate exceeds the basic c.$12 million and the spouse is a noncitizen (i.e., US citizens can leave unlimited assets to their US spouses, with any estate tax deferred until the death of the second spouse, whereas estate tax must be paid immediately on any bequests to noncitizen spouses that end up pushing the estate over the unified gift-and-estate tax credit of c.$12 million). So for us ordinary lot -- noncitizens included -- it's not really necessary to worry too much about US estate tax when the estate is passed on by a US citizen or domiciliary because the unlimited marital deduction is essentially irrelevant unless you happen to be very wealthy indeed (restrictions on gifts to noncitizen spouses and Japanese inheritance tax are different matters). And what happens when a nonresident, noncitizen spouse dies is basically that only in situ US assets are taxed, but the estate-tax exemption is very small, so estate taxes become more likely in that case.
A pretty good recent introduction to gift and estate taxes for noncitizen spouses will be found
here. The implications of the unlimited marital deduction are explained clearly
here. And a good explanation of how US tax residency is determined is given on
this (rather old) page (the information resembles that found in the Deloitte PDF document linked to above.)
Japanese inheritance laws depend upon both nationality and residence, and they make it especially hard for Japanese nationals to escape tax-free. The table on
this page shows the various permutations, which are most beneficial for noncitizens without a Japanese domicile.
By the way, according to the websites of Japanese embassies and consulates in various countries -- including
this one in China, for example -- you can't actually obtain a new reentry permit overseas, but you can apply to a Japanese embassy/consulate for a one-year extension of your current permit if circumstances warrant. In theory, it's possible to spend up to six years overseas (seven years for special permanent residents) on a single multiple-reentry permit without losing PR as long as your residence card remains valid and you can provide a good reason for your extended absence if asked. Company postings, university study, and taking care of relatives would likely all be regarded as good reasons, but less persuasive reasons might eventually raise eyebrows, though it's hard to say. Regular temporary stays overseas, however, would hardly seem to present a problem for a PR who actually maintains tax residency in Japan.
In any case, the recommendation to get professional financial advice seems well worth heeding