I think it is a kind of idealism like that of Berkeley. But can this statement also belong to phenomenology of Husserl or of the philosophy of Kant or is there perhaps a better philosopher for this?
This is known as monist idealism, or idealist monism. Monist, meaning it believes that only one kind of thing actually exists, and idealist, meaning it believes that one thing is mind/consciousness/soul, not matter.
Kant is arguably not a monist (or at least, not committed to monism). He does not deny that the physical world exists (or rather, something that we perceive as the physical world), but only that we can never experience it directly as it "really" is. We interact with it always through the intermediary of our minds.
The word can be idealist monist, but I think Berkeley convinced us that almost all pure and consistent idealism has to be monist. So it is often simply idealist.
I would say Plato is the prime example before Berkeley. Leibniz is another strong option, which I feel is worked out much more reasonably. Whitehead is a revival of Leibniz in some ways, and to that degree is also an idealist.
The two folks you consider are seen as transcendental idealists, suggesting that your body and mind are both projections of 'noumena', something more basic than either.
Kant was trying very hard not to be a simple idealist, and he is the first one to clearly and effectively put this question in the realm of the deeper reality we cannot really be sure of. If we cannot know the deepest forms of reality, at all, how can we know whether they are single or multiple in substance?
For Kant, your body exists in space, which exists only in your mind, so much of the detail about it must to some degree be a projection of the mind. But there is something more basic than space in which some form or precursor of your body and mind might also both exist in some way. You just can't know; because your thinking is trapped in a model that involves space.
Husserl followed him, but emphasized the 'idealistically agnostic' direction even more consistently. The more basic forms are there, but we cannot trust our interactions with them, so we should not rely on any information about them.