Structure of API wrapper
First off:


  The only response i can get from the SOAP client except from data in case of success is exceptions.


Of course, if your call wasn't successful, there's something wrong, and an exception should be thrown. If you query for an ID that doesn't exist, don't catch the exception. That means the user has provided your client with invalid data, and its that user who must deal with the problem. Not You.
An API doesn't really deal with that many exceptions. In fact, I'm one of those people who think that a well written, bug free API-wrapper doesn't need exception handling. If the wrapper/client's code is properly put together, exceptions are the result of either bad usage or exceptions being returned by the webservice. Both types of errors should be dealt with by the user.

If you don't want to pass the client to all those classes, the answer is simple: inheritance:

class BaseClient
{
    protected $client = null;//declare your properties!!!
    protected $config = null;
    //use type hints, default = null means you don't HAVE to pass the argument
    public function __construct(\SoapClient $client = null)
    {
        $this-&gt;client = $client;
    }
    //lazy-loading getter
    protected function getClient()
    {
        if ($this-&gt;client === null)
        {//set client only when it's required
            $this-&gt;setClient(
                new \SoapClient($this-&gt;config['wsdl'], $config['options']
            );
        }
        return $this-&gt;client;
    }
    //public to allow injection
    protected function setClient(\SoapClient $client)
    {
        $this-&gt;client = $client;
        return $this;//makes your api chainable
    }
}


Then define all the classes you'll actually be using along these lines:

class DebptorClient extends BaseClient
{
    protected $config = array(//optional
        'wsdl' =&gt; 'the specific wsdl',
        'options'=&gt; array()//defaults
    );

    public function get($param, $value)
    {
        $client = $this-&gt;getClient();//loads if not yet loaded
        return $client-&gt;Debtor_GetData(
            array(
                'entityHandle' =&gt; $this-&gt;getHandle($param, $value)
            )
        )-&gt;Debtor_GetDataResult;
    }
}


And so on.

Now, some actual code-review:

Declare your properties

From the wrapper tag wiki:


  A wrapper is an OOP technique where an object encapsulates (wraps) another object, hiding/protecting the object and controlling all access to it.


By not declaring $this-&gt;client, client is effectively added later on in your objects life, which means property lookups will be slower, but more importantly: $this-&gt;client will be a public property. If $this-&gt;client is public, then you don't have a wrapper because:


  A wrapper [...] encapsulates another object, hiding/protecting the object and controlling all access to it.


Thus, $this-&gt;client has to be protected or private.
Next.

Seeing this code worries me:

public function getHandle($param, $value)
{
    switch ($param) {
        case 'number':
            return $this-&gt;client-&gt;Debtor_FindByNumber(array('number' =&gt; $value))-&gt;Debtor_FindByNumberResult;
            break;//unreachable statement, btw
        case 'email':
            return $this-&gt;client-&gt;Debtor_FindByEmail(array('number' =&gt; $value))-&gt;Debtor_FindByEmailResult;
}


You're expecting the people who are to use your api to know that $param and $value are expected to be. $param has only 2 valid options: number or email. anything else is invalid, yet at no point to you bother to validate the data you're being passed.
When developing an API wrapper, it's not a bad idea to create Argument models:

namespace Soap\Data;
class Argument
{
    private $type = null;
    private $value = null;
    public function __construct($type, $value)
    {
        $setter = 'set'.ucfirst(trim($type));//email becomes setEmail
        if (!method_exists($setter, $this))
        {
            throw new \InvalidArgumentException($type.' is not a valid type for '.__CLASS__);
        }
        $this-&gt;{$setter}($value);
    }
    public function setEmail($email)
    {
        if (!filter_var($email, \FILTER_VALIDATE_EMAIL))
        {
            throw new \InvalidArgumentException($email.' is not a valid email address');
        }
        $this-&gt;value = $email;
        return $this;
    }
}


This allows you to define methods like this:

public function getByType(Argument $value)


and the Argument class ensures that the data you'll receive is validated properly.

Now, error handling.
That very much depends on how you see your code being used. Is it supposed to be a sort of "module" to be included into various projects, in which case, I'd just throw my exceptions out for the caller to deal with them. Code that is used as a dependency shouldn't have to anticipate all sorts of errors that might occur, that's the users job.

If you want this code to work sort of in the background, You could write your own exceptions (extending from either the base Exception class, or SoapFault) if you wanted to.
You could then register your own exception/error handler and unset/restore the old at lib, and quietly log the exceptions. The user, who will then be left clueless as to what actually went wrong will hate you for this. Having to check the logs constantly is a pain when developing, so add some manual overrides, too

class BaseClient
{
    protected static $exceptions = false;
    public function __construct()
    {
        if (static::$exceptions === false)
        {//static to avoid setting handler more than once
            static::$exceptions = true;
            set_exception_handler(array($this, 'exceptionHandler'));
    }
    public function exceptionHandler(\Exception $e)
    {
        //handle
    }
    public function freeExceptions()
    {
        if (static::$exceptions)
        {
            restore_exception_handler();
            static::$exceptions = false;
        }
    }
    public function __destruct()
    {
        $this-&gt;freeExceptions();
    }
}


That's one way of going about your business. Generally, though, I use the occasional try-catch block, if I've created a method that strings together a series of Soap calls, for example, but most of the time I consider Exceptions best handled by the code that invoked the method where the exception is thrown, not by the code that throws the exception.