When I migrate customizations using Application Composer, would the field-value mappings also migrate?

Use this topic to know how to migrate field value mappings when migrating customizations using Application Composer.

No. You'd need to define the field-value mapping manually after you migrate customizations. Also, after you import a configuration into a target environment, you must examine the target environment for any changes that you might need to make manually

The value mapping here refers to the parent-child value map you create for custom fixed choice list fields. For actual field-value mapping, you must perform data import operation.