Ask the administrator of the first email address to setup a forwarding to the second one. This can be done address by address. On Unix it starts often by a simple .forward
file in home directory.
You are stating you do not want forwarding, but why exactly? Because if you intend to do DNS changes (that will only partially solves the problem as @HomoTechsual shows) that means you control example1.example
in some way (otherwise you won't be able to do any DNS change here), so if you control it why you do not want to set up forwarding on it?
By being so overly generic in your question, you are making it difficult to give you relevant answers, so you probably need to edit your question to be more specific/clear on your constraints. Using non obfuscated names could help too.
If possible, please delete this question. – trnj – 2018-05-11T00:00:01.437