Fluid antenna multiple access (FAMA) is capable of exploiting the high spatial diversity of wireless channels to mitigate multi-user interference via flexible port switching, which achieves a better performance than traditional multi-input-multi-output (MIMO) systems. Moreover, integrated data and energy transfer (IDET) is able to provide both the wireless data transfer (WDT) and wireless energy transfer (WET) services towards low-power devices. In this paper, a FAMA assisted IDET system is studied, where $N$ access points (APs) provide dedicated IDET services towards $N$ user equipments (UEs). Each UE is equipped with a single fluid antenna. The performance of WDT and WET , i.e., the WDT outage probability, the WET outage probability, the reliable throughput and the average energy harvesting amount, are analysed theoretically by using time switching (TS) between WDT and WET. Numerical results validate our theoretical analysis, which reveals that the number of UEs and TS ratio should be optimized to achieve a trade-off between the WDT and WET performance. Moreover, FAMA assisted IDET achieves a better performance in terms of both WDT and WET than traditional MIMO with the same antenna size.