when America was discovered by the Europeans, they sent criminals to colonize it.
Although this (unreferenced) claim has a tiny grain of truth in it, it is grossly misleading.
Numbers of convicts compared to non-convicts
According to one author around 50,000 convicts were transported to North America over a 58-year period before independence.
In 1776 the US population was estimated at 2.5 million. Most of these were not convicts nor the offspring of convicts.
So it is misleading to say that "convicts were sent to colonise [north America]" as most of the people that travelled from Europe to north America were not convicts sentenced to transportation.
Only Britain transported convicts to north America. So it is misleading to say that Europeans did so.
You too are criminal offspring
Almost all Europeans are descendents of Charlemagne and of almost everyone else alive 500 or more years ago. The reason is "if you go back 40 generations, you have over two trillion ancestors!". This also applies to other regions of the world.
Most Europeans share recent ancestors (Nature, 2013):
any two Europeans are likely to have many common ancestors who lived around 1,000 years ago. A genomic survey of 2,257 people from 40 populations finds that people of European ancestry are more closely related to one another than previously thought
Tracing the world's ancestor, Dr Yan Wong, 2012 (reported by BBC):
... imagine the simplest case of a population of a constant size - say a million ...
If people in this population meet and breed at random, it turns out that you only need to go back an average of 20 generations before you find an individual who is a common ancestor of everyone in the population.
If you go back on average 1.77 times further again (35 generations) everyone in the population will have exactly the same set of common ancestors
In fact about 80% of the people at that time in the past will be the ancestors of everyone in the present. The remaining 20% are those who have had no children
It is almost certain that every person on earth is a descendent of a criminal many generations ago.