Finite-dimensional Grassmann-envelope conjecture for identities with involution

Let $F$ be a field of characteristic zero. For an associative $F$-algebra with involution, write

$$E(C)=C_{\bar{0}} \otimes E_{\bar{0}} \oplus C_{\bar{1}} \otimes E_{\bar{1}}$$

for the Grassmann envelope of an associative superalgebra $C=C_{\bar{0}} \oplus C_{\bar{1}}$ with superinvolution.

Grassmann-envelope conjecture. Any associative $F$-algebra with involution satisfies the same $*$-identities as $E(C)$ for some associative superalgebra $C=C_{\bar{0}} \oplus C_{\bar{1}}$ with superinvolution that is finite-dimensional over $F$.

This conjecture seeks to represent the $*$-identities of every associative algebra with involution by the Grassmann envelope of a finite-dimensional superalgebra. The source presents it as an expected analogue of results for superalgebras with superinvolution and gives no evidence of resolution.