If you using Box only for shared data (i.e., you are not using Box for private storage), then it is best to migrate Box shared folders (team folders) to appropriate team SharePoint document libraries.
To migrate Box accounts to Office365 Sharepoint sites, you need to create one-way sync pairs like this:

Box Business (admin@acme.com)/team_folder_HR -> Office365 Sharepoint (admin@acme.com)/HR Site/Documents
Box Business (admin@acme.com)/team_folder_Production -> Office365 Sharepoint (alice@acme.com)/Production Site/Documents
Box Business (admin@acme.com)/team_folder_Finance   -> Office365 Sharepoint (bob@acme.com)/Finance Site/Documents
...

The above will create a one-way sync of each Box team folder with Office365 Sharepoint. The data will be migrated, and it will also be kept in sync—allowing you seamless transition.

cloudHQ will also replicate all sharing information and permissions from Box to Sharepoint.

Here are step-by-step instructions on how to setup data migration sync pairs.

Box Business and Box Enterprise Preparation:

• Ensure that you are a Box for Business admin. The instructions are here: Box for Business admin.
• In some Box installations, third-party applications might be disabled. You will need to check if third-party applications are disabled in your Box account and enable them. Instructions for how to check that are here: https://support.cloudhq.net/how-to-enable-cloudhq-third-party-application-in-box-enterprise/.

Authorize cloudHQ to access your Box Business or Box Enterprise Account

• Go to https://www.cloudHQ.net/services and click the “Box for Business” icon:
  
• Authorize your Box for Business admin email and follow the wizard steps:

  Authorize Box for Business admin account:
  
  

  Add Box for Business accounts:
  

  Box for Business successfully authorized
  

Authorize cloudHQ to access your Office 365 domain

• Go to https://www.cloudHQ.net/services and click the “Office 365” icon:
   
• Accept Office 365 authorization:

  

Create migration sync pairs for each of Box users

1. Start the wizard and select “Single User Setup”:
   
2. In the next page select “Sync Two Clouds”:
   
3. Click on the Box icon
   
4. Authorize Box account and choose migration type (entire account or existing folder):
   
5. Select the Box folder which contains data that needs to migrated to SharePoint, then click “Select”:
   
6. Click on the Office365 Sharepoint icon
   
7. Enter Site name or Site URL to search SharePoint site.
   
8. Select the SharePoint document library or sub-folder or click “Create Folder” to create a new folder, then click “Select”.
   
9. Select the following two options:
   1. Replicate sharing meta-data for files I own Learn more
   2. Sync only files I own (skip all files and folders which are shared with me)

   

10. The synchronization status will display after the initial synchronization
11. Here is How to Monitor Status of Sync.
12. An email will confirm the success of the initial synchronization.