Electron–positron-pair annihilation and other atomic processes stimulated by μ+ decay in the negatively charged muonium ion Mu− (or μ+e−e−) are considered. Most attention is paid to (e+, e−)-pair annihilation, where a positron is produced during the decay of the μ+ muon. It is shown that the probability of two-photon (e+, e−)-pair annihilation P2(γ) is bounded between ≈1.04 × 10−6 and ≈6.91 × 10−6, while the total probability of secondary annihilation can be relatively large, ≈4.5 × 10−4 to 6.0 × 10−4. The radiative decay of μ+ muon, mounium–antimuonium conversion and some other μ+ decay channels are also discussed. In general, the study of muon decay in the muonium Mu− ion can improve our understanding of weak interactions and their role in atomic systems.