This paper studies the inverse problems for identifying space-dependent coefficients and sources in a parabolic system with overspecified conditions at final time. The model of a weakly coupled system of two reaction-diffusion equations for the spatial distribution of uncontaminated and contaminated foraging bees is also discussed as a biological motivation. We propose two approaches for studying the problems. The first one uses the overspecified information to transform the inverse problems into direct (forward) ones for non-linear parabolic equations involving the solution values at the final time in the differential operator and initial conditions. This allows us to prove, using fixed-point arguments, existence of solution to the inverse problems. The second study employs the concept of the quasi-solution to establish existence of solution to the inverse problems as minimizers of least-square cost functionals. The present approach is a base for further computational research.