PIP Claim Timescales

Hello, My brother has just had his letter saying his DLA is ending and asking him to decide whether he wishes to make a claim for PIP. He has to call DWP by 28th June if he wishes to make a claim and I understand that after making this phone call he will receive a form to complete and return in order for DWP to assess his claim. My query is how long does it generally take DWP to send the form that has to be completed after the initial claim telephone call has taken place? Also once you get the form, how long do you have to complete it and send it back?
My reason for asking the question is that I need to help my brother with his claim and I am due to go to USA on 20 June for 4 Weeks and will not be back till 21 July and I am worried that the form will arrive whilst I am away and have to be returned to DWP before I get back. Thank you