The declaration var $b; is PHP 4. PHP 5 allows it and it is equivalent to public $b;.
However, it is deprecated and if you use a proper error reporting (error_reporting(E_ALL); during development) you get a warning about it. You should use the PHP 5 visibility kewords instead.
Also, the declaration function repo($myvar) is a PHP 4 constructor style, also accepted but deprecated. You should use the PHP 5 __constructor() syntax.
You access $b as static::$b and this is not compatible with its declaration (equivalent, as I said above, with public $b). If you want it to be a class property (this is what static does) you have to declare it as a class property (i.e. public static $b).
Putting everything together, the proper way to write your class is:
final class repo {
    // public static members are global variables; avoid making them public
    /** @var \Guzzle\Http\Client */
    private static $b;
    // since the class is final, "protected" is the same as "private"
    /** @var \Guzzle\Http\Client */
    protected $client;
    // PHP 5 constructor. public to allow the class to be instantiated.
    // $myvar is probably a \Guzzle\Http\Client object
    public __construct(\Guzzle\Http\Client $myvar)
    {
        static::$b = $myvar;
        // $this->b probably works but static::$b is more clear
        // because $b is a class property not an instance property
        $this->client = static::$b;
    }
}