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Spiking neural networks are efficient computation models for low-power environments. Spike-based BP algorithms and ANN-to-SNN (ANN2SNN) conversions are successful techniques for SNN training. Nevertheless, the spike-base BP training is slow and requires large memory costs. Though ANN2NN provides a low-cost way to train SNNs, it requires many inference steps to mimic the well-trained ANN for good performance. In this paper, we propose a SNN-to-ANN (SNN2ANN) framework to train the SNN in a fast and memory-efficient way. The SNN2ANN consists of 2 components: a) a weight sharing architecture between ANN and SNN and b) spiking mapping units. Firstly, the architecture trains the weight-sharing parameters on the ANN branch, resulting in fast training and low memory costs for SNN. Secondly, the spiking mapping units ensure that the activation values of the ANN are the spiking features. As a result, the classification error of the SNN can be optimized by training the ANN branch. Besides, we design an adaptive threshold adjustment (ATA) algorithm to address the noisy spike problem. Experiment results show that our SNN2ANN-based models perform well on the benchmark datasets (CIFAR10, CIFAR100, and Tiny-ImageNet). Moreover, the SNN2ANN can achieve comparable accuracy under 0.625x time steps, 0.377x training time, 0.27x GPU memory costs, and 0.33x spike activities of the Spike-based BP model.