How i can choose Integrity skin for my minibb forum?

I found Integrity skin, but i see big mistake. Only one Integrity work properly on new minibb version:) The old skin classic, green and more is no work good:) There i can download old minibb version?

That's correct, but actually we have removed older skins downloads from our website 'cause we don't support them anymore (in general, applying your own skin is the only correct approach when building a serious website). We have only some skins made by 3rd parties.

Here is how to apply any kind of skin to miniBB, incl. Integrity.

And Ivan's Collection of Skins for miniBB 2 not work good with minibb 2.2b to?
This skin pack is not supported with 2.2b version?

If you pay attention to the date when those skins were published, you will see it's 2007, and for sure something is incompatible with the newest version.

However I don't understand your problem... you could just compare the newest skin to the older one, then add missing CSS classes and modify them a bit... it's very simple.