Great question — answering as the UphillTech team:
Yes(ish). But you will need to help them. There are several ways that Google, for example, will relate domain names. 1] Registration information. Make sure that the owner contact of the original and new domain match and that the contact information match. If this is not possible, then do the best you can. If these match, Google will credit the new domain with some small amount of trust and begin to make some assumptions. 2] On-site contact information. It is highly advisable that the About and/or Contact page of each domain contain contact information about the other site (if they differ or the same if they do not) as well as a link. In addition, schema.org mark-up should be used. Mark-up...
Full answer by closetnoc: https://webmasters.stackexchange.com/a/89869 (CC BY-SA 3.0).
Need it done for your business? UphillTech.