Asset list and Certification Audit

Each company should include in its ISMS scope only the assets they control directly - so overlapping of assets means that they didn't set the scope correctly; and sharing the asset list is not necessary if the ISMS scope document is written precisely enough. The certificate of the ISO 27001 is only for 1 organization, so your organization is responsible of the maintenance of his certificate (in terms of his scope). At this point I recommend you to read this arti cle "How to define the ISMS scope”: https://advisera.com/27001academy/knowledgebase/how-to-define-the-isms-scope/

 Also is it possible to develop an SLA between us in such a way that customer's ISO auditors do not carry out an exhaustive audit of our assets. For e.g. can we include the statement in the SLA that the service provider (i.e. us) is ISO 27001 certified and hence we avoid the duplication. We, as service provider, can always produce information to demonstrate compliance though. With the above approach, the customer would still be able to identify themselves as ISO certified.

Answer:

It is necessary to study each situation, but generally in accordance with my last point, each auditor has to audit each ISMS (based on the scope of each one). So, in this scenario you can develop this SLA, but anyway there will be 2 different ISMS, with 2 different scope, and 2 different internal audit + 2 different certification audit.
 
Please, if you need more information, give us more information about your situation (scope of your organization, scope of your customer, etc).