I'm not sure you could have anarcho-communism inside an anarcho-capitalist system.

Say some of the individuals in an anarcho-capitalst society decided to treat all their private property as public means of production and form an anarcho-communist group.
On the surface, it would seem that from the perspective of the capitalists and the free market, the communists could be considered a single entity. However, if you look at it from the communists perspective, they would be subject to control and limitations from the surrounding capitalist environment. Just to present a few issues:
They would have to uphold contracts with external actors. That means, they would have to collectively agree upon the contents of these contracts. They would need to implement some process to choose how their collective interests are represented towards these external actors.
They would be subject to the effects of the free market. As they would not control all available resources, they would have to import and export certain things. For example, if their collective territory did not contain any drinking water, their very existence would be dependent on the capitalist market.

So while I'm sure it would be possible to implement some of the anarcho-communist principles in a closed group within an anarcho-capitalist system, a lot of them would have to be significantly rethought to fit the environment, most likely to the point where it couldn't even be labeled anarcho-communism anymore.
But then again, this would be possible the other way around as well: you could form a group in an anarcho-communist system where members of the group respect each others private property, sign contracts, exchange goods through a free market and as a group (from their perspective, uphold the contract to) collectively take what they need and produce to their abilities. It's probably more obvious to you how this would be a mutilation of the inner group's principles.