Summary: In their famous work, L. Accardi and M. Bożejko [Infin. Dimens. Anal. Quantum Probab. Relat. Top. 1, No. 4, 663–670 (1998; Zbl 0922.60013)] have introduced a surprising convolution among the real probability laws with finite moments of any order, by proving this is universal in the sense that any symmetric such probability law is infinitely divisible with respect to it, and a central limit law. We present a quick generalization of their construction to the so-called Jacobi-Szegő distributions introduced by M. Anshelevich and J. D. Williams [Bull. Sci. Math. 145, 1–37 (2018; Zbl 1398.46052)] in the operator-valued non-commutative frame considered by D. Voiculescu [in: Recent advances in operator algebras. Collection of talks given in the conference on operator algebras held in Orléans, France in July 1992. Paris: Société Mathématique de France. 243–275 (1995; Zbl 0839.46060)] or R. Speicher [Mem. Am. Math. Soc. 627, 88 p. (1998; Zbl 0935.46056)] for the free probability theory [D. V. Voiculescu et al., Free random variables. A noncommutative probability approach to free products with applications to random matrices, operator algebras and harmonic analysis on free groups. Providence, RI: American Mathematical Society (1992; Zbl 0795.46049)].