Ultra-intense lasers can nowadays routinely accelerate kiloampere ion beams. These unique sources of particle beams could impact many societal (e.g., proton-therapy or fuel recycling) and fundamental (e.g., neutron probing) domains. However, this requires overcoming the beam angular divergence at the source. This has been attempted, either with large-scale conventional setups or with compact plasma techniques that however have the restriction of short (<1 mm) focusing distances or a chromatic behavior. Here, we show that exploiting laser-triggered, long-lasting (>50 ps), thermoelectric multi-megagauss surface magnetic (B)-fields, compact capturing, and focusing of a diverging laser-driven multi-MeV ion beam can be achieved over a wide range of ion energies in the limit of a 5° acceptance angle.