The recent advances in low earth orbit (LEO) satellite-borne edge cloud (SEC) enable resource-limited users to access edge servers via a terrestrial station terminal (TST) for rapid task processing capability. However the dynamic variation in the TST transmit power challenges the served users to develop optimal computing task processing decisions. In this paper we propose an efficient pruning-split long short-term memory (LSTM) learning algorithm to address this challenge. First we present an LSTM algorithm for TST transmit power prediction. The proposed algorithm is then pruned and split to decrease the computing workload and the communication resource consumption considering the limited computing resource of TSTs and served users' quality of service (QoS). Finally an algorithm split layer selection method is introduced based on the real-time situation of the TST. The simulation results are shown to verify the effectiveness of the proposed pruning-split LSTM algorithm.