There is no default recommended way to achieve this, but you do have three methods at least to choose from.
You'll need the SMS Message Detail report imported to your Data Extension in order to work with the SMS data as it contains the SubscriberKey attribute amongst others you'll be using.
Automation Studio - you'll be writing a Code Snippet block that creates a new MobileHistoryLog (or whatever the object is called) in Sales Cloud by using CreateSalesforceObject function.
For first activity you'll have SQL query running and posting daily/hourly results to a new target Data Extension and always overwriting the content.
Followed by the Script Activity to initiate SSJS to trigger an AMPscript block that uses your DE to create the SMS history records in Sales Cloud.
Journey Builder - if you don't feel confident with AMPscript then you can use the automated Data Extension as source for the Journey. The Journey would be utilizing the Object Activity to create new SMS history records for the contacts that enter this Journey.
Custom API - if you have development resources you can use the Data Extension as source to create/update Sales Cloud records directly, real-time via API's.
As a side comment - from what I've seen posted on community groups, the method of storing SMS History logs is on Marketing Cloud roadmap as an official feature. Though it may not happen this year, or even next.