Can a supplier fake the capacity? Like label 100Ah but deliver less?

Unfortunately, yes — it happens. Some batteries are labeled with nominal capacity but deliver less usable energy, or use a lower Depth of Discharge (DoD) so you can only use 80% safely. Always ask for the usable capacity and the tested cycle life, not just the headline number. A trustworthy supplier provides the datasheet and test report; a suspicious one gives vague answers.