Cooperative edge offloading to nearby end devices via Device-to-Device (D2D) links in edge networks with sliced computing resources has mainly been studied for end devices (helper nodes) that are stationary (or follow predetermined mobility paths) and for independent computation tasks. However, end devices are often mobile, and a given application request commonly requires a set of dependent computation tasks. We formulate a novel model for the cooperative edge offloading of dependent computation tasks to mobile helper nodes. We model the task dependencies with a general task dependency graph. Our model employs the state-of-the-art deep-learning-based PECNet mobility model and offloads a task only when the sojourn time in the coverage area of a helper node or Multi-access Edge Computing (MEC) server is sufficiently long. We formulate the minimization problem for the consumed battery energy for task execution, task data transmission, and waiting for offloaded task results on end devices. We convert the resulting non-convex mixed integer nonlinear programming problem into an equivalent quadratically constrained quadratic programming (QCQP) problem, which we solve via a novel Energy-Efficient Task Offloading (EETO) algorithm. The numerical evaluations indicate that the EETO approach consistently reduces the battery energy consumption across a wide range of task complexities and task completion deadlines and can thus extend the battery lifetimes of mobile devices operating with sliced edge computing resources.