Range filters are probabilistic data structures that answer approximate range emptiness queries. They aid in avoiding processing empty range queries and have use cases in many application domains such as key-value stores and social web analytics. However, current range filter designs do not support dynamically changing and growing datasets. Moreover, several of these designs also exhibit impractically high false positive rates under correlated workloads, which are common in practice. These impediments restrict the applicability of range filters across a wide range of use cases. We introduce Memento filter, the first range filter to offer dynamicity, fast operations, and a robust false positive rate guarantee for any workload. Memento filter partitions the key universe and clusters its keys according to this partitioning. For each cluster, it stores a fingerprint and a list of key suffixes contiguously. The encoding of these lists makes them amenable to existing dynamic filter structures. Due to the well-defined one-to-one mapping from keys to suffixes, Memento filter supports inserts and deletes and can even expand to accommodate a growing dataset. We implement Memento filter on top of a Rank-and-Select Quotient filter and InfiniFilter and demonstrate that it achieves competitive false positive rates and performance with the state-of-the-art while also providing dynamicity. Due to its dynamicity, Memento filter is the first range filter applicable to B-Trees. We showcase this by integrating Memento filter into WiredTiger, a B-Tree-based key-value store. Memento filter doubles WiredTiger's range query throughput when 50% of the queries are empty while keeping all other cost metrics unharmed.