Here's what BBB has to say:

The BBB review should be sufficient to make anyone think twice before subjecting themselves to Apple Movers:

Based on BBB files, this business has a BBB Rating of F on a scale from A+ to F.
Reasons for this rating include:

* BBB does not have sufficient information to determine how long this business has been operating.
* BBB does not have sufficient background information on this business.
* Failure to respond to one complaint filed against business.
* One complaint filed against business that was not resolved.

[snip]

Customer Complaint History

When considering complaint information, please take into account the company's size and volume of transactions, and understand that the nature of complaints and a firm's responses to them are often more important than the number of complaints.

BBB processed a total of 2 complaints about this company in the last 36 months, our standard reporting period. Of the total of 2 complaints closed in 36 months, 2 were closed in the last year.
These complaints concerned :
+ 1 regarding Billing or Collection Issues

1 - None of the Above - Credit, Billing or Collection Complaint Issue
+ 1 regarding Delivery Issues

1 - None of the Above - Delivery Complaint Issue

These complaints were closed as:
+ 1 No Response

1 - Company failed to respond to BBB to resolve or address the complaint issues.
+ 1 Unresolved