A duality is made explicit between K-records of i.i.d sequences of observations and records in the F-scheme. Via the Sakhanenko Lemma, we establish strong invariance principles for partial sums   of independent random variables. We consider as applications of our main results the case of K-records. Afterwards, by making use of strong approximations of Markov chains, we establish invariance principles for records in a dual model: the F-scheme. For both models limit results related to numbers of records are given.