Dynamic Scene Graph Generation (DSGG) aims to create a scene graph for each video frame by detecting objects and predicting their relationships. Weakly Supervised DSGG (WS-DSGG) reduces annotation workload by using an unlocalized scene graph from a single frame per video for training. Existing WS-DSGG methods depend on an off-the-shelf external object detector to generate pseudo labels for subsequent DSGG training. However, detectors trained on static, object-centric images struggle in dynamic, relation-aware scenarios required for DSGG, leading to inaccurate localization and low-confidence proposals. To address the challenges posed by external object detectors in WS-DSGG, we propose a Temporal-enhanced Relation-aware Knowledge Transferring (TRKT) method, which leverages knowledge to enhance detection in relation-aware dynamic scenarios. TRKT is built on two key components:(1)Relation-aware knowledge mining: we first employ object and relation class decoders that generate category-specific attention maps to highlight both object regions and interactive areas. Then we propose an Inter-frame Attention Augmentation strategy that exploits optical flow for neighboring frames to enhance the attention maps, making them motion-aware and robust to motion blur. This step yields relation- and motion-aware knowledge mining for WS-DSGG. (2) we introduce a Dual-stream Fusion Module that integrates category-specific attention maps into external detections to refine object localization and boost confidence scores for object proposals. Extensive experiments demonstrate that TRKT achieves state-of-the-art performance on Action Genome dataset. Our code is avaliable at https://github.com/XZPKU/TRKT.git.