FAQ: is it possible that a gene has a different expression after genetic introgression (transmutation)?
For a start: The expression of the gene will depend on a lot of factors so there isn’t just one answer to this. In a more scientific term the expression means how the gene is transcribed and translated, spliced etc.
In genetic introgression, they breed one specific gene (in aviculture mainly a colour mutation) from one species into another, closely related, species. So they transfer the genetic material from one species into the gene pool of another. The whole process takes several generations of repeated backcrossing of an interspecific hybrid with one of its parent species.
Because they transfer genetic material from one species into another, it is always possible that one of both species contains a gene that can influence the expression of a certain trait or, most interesting in aviculture, the expression of a mutation. We call this epistasis and such a gene we call an epistatic gene or a modifier gene.
In epistasis we see that the presence of a mutated gene on a different locus, even on a different chromosome, influences the expression of another, present mutation . This is mainly the case when both genes are involved in the production of the same chemical . Epistasis can express itself in several ways: dominant, recessive, reciprocal ….. BTW: There are also many indications that epistasis plays an important role in the origin of species. 
To illustrate it a little better I would like to use here the example of mutations in domestic pigeons [Columba livia]. We have the sex-linked Tyrp1 gene that is responsible for the basic colours blue, brown and red in pigeons. On an autosomal chromosome we then have the Sox10 gene (involved in the development of melanocytes). That gene is dominantly epistatic over Tyrp1. The presence of that mutated gene therefore influences the expression of the Tyrp1 gene. That is, if a particular variant of the autosomal Sox10 locus is present (and since it is dominant, one allele is sufficient), the present alleles (both blue, brown or red) of the Z-linked Tyrp1 gene do not matter and the colour, in that case, is always red , .
If you ask me if it can change the inheritance pattern of a gen, we don’t think it will change, because the gene will be conserved between the two species. The gene would stay conserved as it was in the original species, else it won’t be able to be expressed. We don’t know of any publications of it, but we doubt that it would change . But the presence of other mutations can always overrule some processes or block some genes. In combination with other mutations it can give us the (wrong) impression that the inheritance pattern of that typical gene has changed
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Dr. Henriette van der Zwan (personal correspondence)’, Nov. 10, 2021