Edge computing is a recent computing paradigm that brings cloud services closer to the client. Among other features, edge computing offers extremely low client/server latencies. To consistently provide such low latencies, services need to run on edge nodes that are physically as close as possible to their clients. Thus, when a client changes its physical location, a service should migrate between edge nodes to maintain proximity. Differently from cloud nodes, edge nodes are built with CPUs of different Instruction Set Architectures (ISAs), hence a server program natively compiled for one ISA cannot migrate to another. This hinders migration to the closest node. We introduce H-Container, which migrates natively-compiled containerized applications across compute nodes featuring CPUs of different ISAs. H-Container advances over existing heterogeneous-ISA migration systems by being a) highly compatible – no source code nor compiler toolchain modifications are needed; b) easily deployable – fully implemented in user space, thus without any OS or hypervisor dependency, and c) largely Linux compliant – can migrate most Linux software, including server applications and dynamically linked binaries. H-Container targets Linux, adopts LLVM, extends CRIU, and integrates with Docker. Experiments demonstrate that H-Container adds no overhead on average during program execution, while between 10ms and 100ms are added during migration. Furthermore, we show the benefits of H-Container in real scenarios, proving for example up to 94% increase in Redis throughput when unlocking heterogeneity.