We investigate the integration of stacked intelligent metasurfaces (SIMs) into cell-free massive multiple input multiple output (CF-mMIMO) system to enhance the simultaneous wireless information and power transfer (SWIPT) performance. Closed-form expressions for the spectral efficiency (SE) of the information-decoding receivers (IRs) and the average sum of harvested energy (sum-HE) at the energy-harvesting receivers (ERs) in the novel system model are derived to subsequently formulate a maximum total average sum-HE problem under a minimum SE threshold per each IR. This problem jointly optimizes the SIM phase-shift (PS) configuration and access points' (APs) power allocation, relying on long-term statistical channel state information (CSI). This non-convex problem is then transformed into more tractable forms. Then, efficient algorithms are proposed, including a layer-by-layer heuristic method for SIMs PS configuration that prioritizes sum-HE for the ERs and a successive convex approximation (SCA)-based power allocation scheme to improve the achievable SE for the IRs. Numerical results show that our proposed algorithms achieve an almost 7-fold sum-HE gain as we increase the number of SIM layers, while the proposed power allocation (PPA) scheme often gains up to 40% in terms of the achievable minimum SE, compared to the equal power allocation.