Traditionally, mobile wallets rely on a trusted server that provides them with a current view of the blockchain, and thus, these wallets do not need to validate the header chain or transaction inclusion themselves. If a mobile wallet were to validate a header chain and inclusion of its transactions, it would require significant storage and performance overhead, which is challenging and expensive to ensure on resource-limited devices, such as smartphones. Moreover, such an overhead would be multiplied by the number of cryptocurrencies the user holds in a wallet. Therefore, we introduce a novel approach, called FeatherWallet, to mobile wallet synchronization designed to eliminate trust in a server while providing efficient utilization of resources. Our approach addresses the challenges associated with storage and bandwidth requirements by off-chaining validation of header chains using SNARK-based proofs of chain extension, which are verified by a smart contract. This offers us a means of storing checkpoints in header chains of multiple blockchains. The key feature of our approach is the ability of mobile clients to update their partial local header chains using checkpoints derived from the proof verification results stored in the smart contract. In the evaluation, we created zk-SNARK proofs for the 2, 4, 8, 16, 32, and 64 headers within our trustless off-chain service. For 64-header proofs, the off-chain service producing proofs requires at least 40 GB of RAM, while the minimal gas consumption is achieved for 12 proofs bundled in a single transaction. We achieved a 20-fold reduction in storage overhead for a mobile client in contrast to traditional SPV clients. Although we have developed a proof-of-concept for PoW blockchains, the whole approach can be extended in principle to other consensus mechanisms, e.g., PoS.