Why can a Restricted Boltzmann Machine reconstruct using same weights?

Commonly NN (autoencoders) use a set of weights in the reduction process and another in the reconstruction process.

But a RBM uses the same weights in construction and reconstruction process. I don't think that it can create inverse function of construction using the same weights.

Why can Restricted Boltzmann Machines reconstruct using the same weights?

Restricted Boltzmann Machines are particular generative models. When you define the model with some parameters (weights, bias...) this means that you put in an energy function and you define the joint law of the visible and hidden layer $$p(\mathbf{v},\mathbf{h})$$. This is the first step.
Then, this law contains enough information to deduce $$p(\mathbf{h}|\mathbf{v})$$ and $$p(\mathbf{v}|\mathbf{h})$$ which are used in the reconstruction process.