You don't. The customer asks for a full copy of their data. And then passes it on to you. And then you accept whatever format you get it in and write a script to migrate it to your system.
If you anticipate winning more customers from this vendor, you write that script to be re-usable in the future. And you write another one each time you displace a competitive vendor.
Eventually, you have a library of scripts and can start marketing how smoothly and quickly you can migrate new customers off those vendors.
If you anticipate winning more customers from this vendor, you write that script to be re-usable in the future. And you write another one each time you displace a competitive vendor.
Eventually, you have a library of scripts and can start marketing how smoothly and quickly you can migrate new customers off those vendors.