  We prove that V. Lafforgue's global Langlands correspondence is compatible
with Fargues-Scholze's semisimplified local Langlands correspondence. As a
consequence, we canonically lift Fargues-Scholze's construction to a
non-semisimplified local Langlands correspondence for positive characteristic
local fields. We also deduce that Fargues-Scholze's construction agrees with
that of Genestier-Lafforgue, answering a question of Fargues-Scholze, Hansen,
Harris, and Kaletha. The proof relies on a uniformization morphism for moduli
spaces of shtukas.
