Different processors may have different requirements around how to ask for a data export. Some charge a fee for the export service and some require certain forms to be filled out.
A good approach is to start by sending their support team something like this:
I’d like to export my customer and payment method data from my account with you for import into Stripe.
Stripe is a PCI Level 1 Service provider, so they have security protocols in place for handling data carefully. Stripe’s PCI Attestation of Compliance (AoC) is available upon request, if you don’t already have it on file. For security, Stripe requires that the data export is encrypted with their PGP key, which can be found here: https://stripe.com/docs/security/pgp-migration-key
Stripe’s team will provide me with SFTP server credentials, which I will share with you, so your team can upload my data to Stripe’s server. Please let me know what my next steps are for getting the export process started.