Is it wrong to report less than what something costs so as to pay less tax?

Answer:

"And you shall take no bribe, for a bribe blinds the discerning and perverts the words of the righteous" (Exodus 23:8).

"He who is greedy for gain troubles his own house, but he who hates bribes will live" (Proverbs 15:27).

"A wicked man accepts a bribe behind the back to pervert the ways of justice" (Proverbs 17:23).

"The king establishes the land by justice, but he who receives bribes overthrows it" (Proverbs 29:4).

I'm assuming that your supplier is still asking you to pay the full amount, but she is offering to change the paperwork to make it look like you paid less. This is lying and stealing from your government. "Render therefore to all their due: taxes to whom taxes are due, customs to whom customs, fear to whom fear, honor to whom honor" (Romans 13:7). I understand the desire to pay less in taxes but do so legally. I would not be surprised to learn that since the invoice doesn't reflect the truth that the woman's employer is not always getting what is owed to them from her sales.

The custom's officer is stealing from his employer, the government. By generating no paperwork he is lying about what is coming through his office. He is getting you to share in his crime by indirectly paying you by letting you keep half of what you should have paid. Again, what is going on is sinful.

I know that as a small businessman that every savings is critical to the success of your business. Sometimes doing the right thing creates hardships, especially if some of your competitors are not being as honest as Christ demands of you. However, in the long run, you will be better off. People who cheat the government eventually get caught one way or another. It would be better that you are not sharing in their punishment because you no longer share in their sins.