Answer
Yes, when moving with medications such as antidepressants, it is better to have a prescription. This reduces the risk of questions during transport and later helps explain to a local doctor exactly what the person is taking.
A prescription is especially important for medications that cannot simply be replaced with an over-the-counter remedy. The medication name, dosage, dosing regimen, and, if possible, a clear medical rationale are needed to avoid interrupting treatment after arrival.
A supply for the first few months is useful, but it does not solve the issue in the long term. After moving, you will still need to integrate into the local healthcare system, seek medical advice, and find out whether the same medication is available or a local equivalent with a different brand name and dosage is needed.