Extending surjective maps preserving the norm of symmetric kubo-ando means

Recently, the question of whether surjective maps preserving the norm of a symmetric Kubo-Ando mean can be extended to Jordan $\ast$-isomorphisms has been tackled. The question was affirmatively answered for surjective maps between $C^{\ast }$-algebras for certain specific classes of symmetric Kubo-Ando means. Here, we give a comprehensive answer to this question for surjective maps between $A{W}^{\ast }$-algebras preserving the norm of any symmetric Kubo-Ando mean.