Write something in two places at once

Question

The crux of my question is essentially what's in the title. I shall elaborate more now.

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The Problem

I am planning on writing notes for a math course I had taken and I want it to be a summary of sorts which I can quickly refer to, in the future.
Due to this, I wish to write it in a way that I have all my Definitions, Theorems, Lemma, et cetera in one place without proofs in the middle.

However, I do want to include proofs at the end, for the times I want a more in-depth recap. Therefore, I wish to add a section at the end which would have the proofs as well.

Here is how I want the structure to be:

Section 1. The Quick Recap
 Theorem 1. Riemann Hypothesis
 // other theorems, definition, et cetera 
 //...

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Section 2. The Proofs
 Theorem 1. Riemann Hypothesis
 Proof. // Proof of Theorem 1.

Getting back to the title, the Theorems are exactly what I'd want to be written twice. Of course, I could just copy and paste every single one but I feel like there should be a better alternative. (Especially if I wish to make changes later.) In particular, the numbering should be the same.

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My Thoughts

I believe it's considered good practice to show what I've researched, so I have written a possible attempt of my own.
However, I am completely fine if your solution has something completely different. (In particular, you may skip this section.)

I do have an idea of sorts of what command definition could help me solve this problem but I have no idea how to actually write one. Here is the way I think it could possibly be solved:

We define a command copy which accepts two arguments: text and label. The text would contain the thing that is to be copied. In the above example, it would be "Theorem 1." (and its statement). The label would be the identifier that will help me reference it later. (Similar to how we have \label{} and \ref{}.)

Conversely, we could define a command paste which takes one argument - label. Naturally, this would be the label that would help me refer to the original text and then display it.

A possible error - If I use a countered environment in text (like for Theorems or Lemmas), I fear that it while pasting it blindly, it might actually update the counter and renumber the theorem. I wouldn't want something like this. While I could just reset the counter before the Proofs section, this would pose a problem if I skip the proofs of some theorems in between.

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MWE

I am aware that usually, people prefer if an MWE is given but I think that that should not be required in this case. I will be using the document class article and the standard math packages.

I hope that I've been clear with what I want. I have tried to keep it as bare as possible.

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Additional requirement

Here I describe an additional requirement which I would appreciate. However, it is okay if your answer does not have this.

The requirement is:
In section 1, I would like the text "Theorem 1." to be hyperlinked to take me to the proof of "Theorem 1." in section 2. Conversely, the "Theorem 1." in section 2 should be hyperlinked to bring me back.