Abstract: The Heisenberg product is an associative product defined on symmetric functions which interpolate between the ordinary product and the Kronecker product. Heisenberg coefficients are Schur structure constants of the Heisenberg product and generalization of both Littlewood-Richardson coefficients and Kronecker coefficients. In 1938, Murnaghan discovered that the Kronecker product of two Schur functions stabilizes. In 2014, Stembridge introduced the notion of stability for Kronecker triples which generalize Murnaghan's classical stability result. Sam and Snowden proved a conjecture of Stembridge characterizing stable Kronecker triples. I will show an analogous result for Heisenberg coefficients. I will also show how to construct Heisenberg stable triples using additive matrices. Please email Colleen at cer2 (at) illinois (dot) edu for the Zoom ID and password.