I assume you're asking for Japanese inheritance tax purposes (i.e. to avoid tax). If so, she'll need adequate proof of at least
five years of continuous overseas residence, as I understand it.
It's at least fairly hard to work in Singapore, in an office, without physically being in Singapore. So one possible approach is that she could obtain a letter from her employer attesting to her regular physical attendance, assuming that was the case.
Her IRAS Notices of Assessment should include the fact she was taxed at the resident rate rather than the non-resident rate, and that should be helpful.
She can
ask the Ministry of Manpower if they'll issue a letter of some kind attesting to her pass history.
The
Immigration and Checkpoints Authority might be able to provide her with an official record of her entries into and exits from Singapore. If her passport was renewed at any point over the past few years she should also provide her previous passport details when making this request. I'm assuming she spent most of her time in Singapore and didn't travel much, and so a record of her entries and exits would help support a residence determination (as the Japanese define it).
If she registered her presence in Singapore with the Japanese embassy then that'd be helpful, so that's another record she could collect.
Her bank and credit card statements should provide some evidence of physical presence in Singapore, showing merchants and ATMs in Singapore.
Facebook and other social media, if she used them, can also provide evidence. Other possible pieces of evidence include class attendance and course completion records, medical appointment records, frequent flyer records (with short trips outside Singapore and consistent returns into Singapore).... basically anything that shows Singapore attachments.