In 1639 he moved to Paris, and in 1649 he became Royal Swedish engraver for Queen Christina in Sweden until 1654, when she became a Catholic.

Jeremias' brother Hans Falck was a Messerschmidt (knife smith) at Neugarten, Danzig.

Falck's work was admired and used by publisher Georg Forster, such as engraved illustrations for "Selenography" of Johannes Hevelius and "Orationes" of Jerzy Ossoliński, Great Crown Chancellor of the Polish–Lithuanian Commonwealth.

The 1890 book with dedication by the great-grandson Herman Eugen Falk thanks a number of Polish writers who collected works by Falck.

Of about three hundred portraits and pictures, which were personally inspected by J.C. Block for his book, nearly all works show J. Falck, sculp., but there are some that identify him as Swedish sculptor, when he was in salaried employment in Sweden.