arXiv:2610.30923v1 Announce Type: new Abstract: Space data centers (SpaceDCs) are emerging as platforms for large language models (LLMs), supported by continuous solar-energy harvesting and high-speed interconnections. The mixture-of-experts (MoE) architecture supports distributed LLM inference by deploying experts across satellites. However, skewed expert activation creates uneven computation power demands despite uniform solar-power supply at the dawn-dusk sun-synchronous orbit (SSO). Consequently, active experts remain power-constrained while harvested power at idle experts is underused. These reduce inference efficiency and increase latency. To address this supply-demand mismatch, we propose the SpaceWPT framework, which uses inter-satellite laser-based wireless power transfer (WPT) to redistribute harvested power. The key design challenge is to balance the computation demands of power-donating and power-receiving satellites under WPT losses: transferring more power accelerates computation at the receiver but leaves less power for the donor. After deriving design principles that simplify WPT control, we characterize the resulting latency tradeoff through a tractable surrogate of average inference latency. Minimizing the surrogate yields a novel two-sided water-filling strategy that determines whether each active expert donates, retains, or receives power according to the water level and its WPT link efficiency. Simulations with Mixtral-8x7B and Phi-3.5-MoE show up to 29.25% lower inference latency than without WPT, with larger gains under more compact formations and higher transfer efficiencies.