Satellite networks play a vital role in providing global connectivity to remote areas, including mountains, forests, and regions affected by natural disasters. The primary challenge lies in the limited communication timeframe between satellites and earth stations (ESs) due to the swift motion of satellites, making timely satellite data downloads through ESs challenging. To address this, we propose a method named Priority-Aware and Throughput-Optimized Inter-Satellite Cooperative Data Transmission (PACT). PACT optimizes network throughput while maximizing download priorities for ESs by leveraging inter-satellite links (ISLs), considering diverse download priorities for different data types. To comprehensively capture constellation characteristics, PACT models low earth orbit (LEO) constellations using a spatiotemporal graph. Within the graph, data priorities are assigned as edge weights, and the allocation of initial download windows to ESs is achieved by maximum weighted matching. Subsequently, PACT organizes a contact plan through cooperative scheduling leveraging ISLs. A bipartite graph is constructed based on data awaiting download and link allocation to redistribute remaining download windows optimally through maximum matching. This iterative process enhances network throughput and maintains data priority. Performance assessments in the ndnSIM framework, covering diverse load scenarios, demonstrate the efficiency and benefits of PACT, particularly in prioritizing data downloads.