In dynamic positron emission tomography (PET), both standard uptake value (SUV) and standard tumor-to-blood uptake ratio (SUR) are sensitive to scan time, and inconsistent uptake time might lead to inaccurate metabolism quantification. To overcome the limitations in the current analytical method or deep learning models for uptake time correction, we propose a time-aware generative adversarial network (GAN)-based method to correct SUVs of dynamic frames at a different uptake time to the reference time (60-minute). Specifically, the uptake time of the input frame is encoded and embedded into the bottleneck of the generator through a learnable representation and feature-wise linear modulation, and the temporal 2.5D input along the time dimension provides essential time- and kinetics-related context to the model. On a real-patient dataset, the proposed model demonstrated its ability to predict the dynamic frame at the reference time from a different uptake time with desirable visual performance, high quantitative image similarity measurements, and comparable SUV and SUR distributions, outperforming other analytical and generative baselines. The nuclear medicine expert's review of the readings noted comparable visual and noise patterns, along with identified lesions showing no change in interpretation. The potential to shorten the current clinical workflow by reducing uptake time is suggested.