I am reading about Signing vs. Public-Key encryption and a question pop up in mind that is it possible to transform any signature scheme to a public-key encryption scheme?
No, we know no general way to build a public-key encryption scheme from a signature scheme.
And accordingly, we have some signature schemes with no known way to build a public-key encryption scheme from the same primitives. An example is the eXtended Merkle Signature Scheme, built from symmetric hash and PRF.
[It was not asked, but: I learned from Maeher's comment that we can build a signature scheme from any public key encryption scheme. And I can't tell from memory a public-key encryption scheme that does not have a related signature scheme built from similar primitives or underlying problem(s)].