Finally, after a lot of tests, it worked, without the PHP SDK. This is the step by step guide:
Get permissions and the page token:
Go to https://developers.facebook.com/tools/explorer/ and select your app from the first drop down menu, in the left.
Click on the button "Get access token", and in the "Select Permissions" window, click in "Extended Permissions" and check manage_pages and publish_stream, and click in "Get Access Token" blue button.
You may be asked in this step to garant permissions to your app to access to your Facebook account, accept.
Next, click at the end of the text field next to the "GET" drop down, and replace the numbers for: me/accounts, and click in the blue button next to this text field.
You'll get the tokens for all your pages, including your app page. Find your page name in the list, will look like this: "name": "Your page name"
When you located your page, copy the access token for the page (will be really long), that can look like this: "access_token": "XXXXXXXX". Also copy the id of the page: "id": "XXXXX".
That's all for this step, we can start coding now.
Post to your page wall via PHP
First, for this script, you'll need a server supporting curl.
We start the PHP document defining the page access token and the page id that we've get in the 1st step:
<?php
$page_access_token = 'XXXXXXX';
$page_id = 'YYYYYYYY';
After that, we create an array with the info to post to our page wall:
$data['picture'] = "http://www.example.com/image.jpg";
$data['link'] = "http://www.example.com/";
$data['message'] = "Your message";
$data['caption'] = "Caption";
$data['description'] = "Description";
You can of course, use any other post parameter described in https://developers.facebook.com/docs/reference/api/post/ and if you don't need one or many of the parameters above you can simply delete it.
Ok, At this point we add to the array the access token:
$data['access_token'] = $page_access_token;
And we set our post url, to post in our page:
$post_url = 'https://graph.facebook.com/'.$page_id.'/feed';
And the last step, we'll use a curl to post our message in our page wall:
$ch = curl_init();
curl_setopt($ch, CURLOPT_URL, $post_url);
curl_setopt($ch, CURLOPT_POST, 1);
curl_setopt($ch, CURLOPT_POSTFIELDS, $data);
curl_setopt($ch, CURLOPT_RETURNTRANSFER, 1);
$return = curl_exec($ch);
curl_close($ch);
?>
After that, we can save our php document, and try to execute it. The post may appear in our Facebook page.