In this work, we are interested in a function-on-function linear model in which the response and the covariate are partially observed curves. First, we reconstruct the missing part of the covariate using the observed parts. Then, we consider two strategies for dealing with the missing part of the response. The first one consists in a reconstruction in the same way as for the covariate. The second one uses regression imputation. Once the dataset is reconstructed, we estimate the slope function and give the mean square prediction error for a new observation of the covariate. Both methods are compared from a theoretical and a practical point of view.