Free-space optical (FSO) communication has emerged as a promising technology for inter-satellite links (ISLs) due to its high data rate, low power consumption, and reduced interference. However, the performance of inter-satellite FSO systems is highly sensitive to beam misalignment. While pointing-ahead angle (PAA) compensation is commonly employed, the effectiveness of PAA compensation depends on precise orbital knowledge and advanced alignment hardware, which are not always feasible in practice. To address this challenge, this paper investigates the impact of beam misalignment on inter-satellite FSO communication. We derive a closed-form expression for the cumulative distribution function (CDF) of the FSO channel under the joint jitter and misalignment-induced pointing error, and introduce a truncated CDF formulation with a bisection algorithm to efficiently compute outage probabilities with guaranteed convergence and minimal computational overhead. To make the analysis more practical, we quantify displacement based on orbital dynamics. Numerical results demonstrate that the proposed model closely matches Monte Carlo simulations, making the proposed model highly useful to design inter-satellite FSO systems in practice.