A remark on absolutely convergent series in spaces of germs of analytic functions

It is proved that each absolutely convergent series in the space of germs of all analytic functions on a some set $M\subset\mathbb C^N$ endowed with the projective topology converges absolutely in the Fr\''echet space of analytic functions on an open neighborhood of $M$. In particular, this allows us to remove the assumptions about the growth of exponents of exponential series, posed in some previous statements.