  The Functional Linear Model with Functional Response (FLMFR) is one of the
most fundamental models to assess the relation between two functional random
variables. In this paper, we propose a novel goodness-of-fit test for the FLMFR
against a general, unspecified, alternative. The test statistic is formulated
in terms of a Cram\'er-von Mises norm over a doubly-projected empirical process
which, using geometrical arguments, yields an easy-to-compute weighted
quadratic norm. A resampling procedure calibrates the test through a wild
bootstrap on the residuals and the use of convenient computational procedures.
As a sideways contribution, and since the statistic requires a reliable
estimator of the FLMFR, we discuss and compare several regularized estimators,
providing a new one specifically convenient for our test. The finite sample
behavior of the test is illustrated via a simulation study. Also, the new
proposal is compared with previous significance tests. Two novel real datasets
illustrate the application of the new test.
