Classification of subbundles on the Fargues-Fontaine curve

We completely classify all subbundles of a given vector bundle on the Fargues-Fontaine curve, where by a subbundle we mean a locally free subsheaf. Our classification is given in terms of a simple and explicit condition on Harder-Narasimhan polygons. Our proof is inspired by the proof of the main theorem in our previous work (Hong 2019), but also involves a number of nontrivial adjustments.