Owing to the impressive general intelligence of large language models (LLMs), there has been a growing trend to integrate them into recommender systems to gain a more profound insight into human interests and intentions. Existing LLMs-based recommender systems primarily leverage item attributes and user interaction histories in textual format, improving the single task like rating prediction or explainable recommendation. Nevertheless, these approaches overlook the crucial contribution of traditional collaborative signals in discerning users' profound intentions and disregard the interrelatedness among tasks. To address these limitations, we introduce a novel framework known as CKF, specifically developed to boost multi-task recommendations via personalized collaborative knowledge fusion into LLMs. Specifically, our method synergizes traditional collaborative filtering models to produce collaborative embeddings, subsequently employing the meta-network to construct personalized mapping bridges tailored for each user. Upon mapped, the embeddings are incorporated into meticulously designed prompt templates and then fed into an advanced LLM to represent user interests. To investigate the intrinsic relationship among diverse recommendation tasks, we develop Multi-Lora, a new parameter-efficient approach for multi-task optimization, adept at distinctly segregating task-shared and task-specific information. This method forges a connection between LLMs and recommendation scenarios, while simultaneously enriching the supervisory signal through mutual knowledge transfer among various tasks. Extensive experiments and in-depth robustness analyses across four common recommendation tasks on four large public data sets substantiate the effectiveness and superiority of our framework.