Is it permissible for a worshiper to move forward or backward to pick up the phone, or to raise his voice in recitation, in order to inform the caller that he is praying, by analogy with opening the door for a knocker or raising one’s voice for him, when the phone rings for a long time during prayer?

It is permissible for a worshipper to answer the phone if it rings, and to move slightly if necessary, provided he remains facing the Qibla and says "SubhanAllah" (Glory be to Allah) to alert the caller. This is supported by the actions of the Prophet, peace and blessings be upon him, when he carried Umamah, his granddaughter's daughter, during prayer, and when he opened the door for Aisha while he was praying, and his command for men to say "Tasbeeh" (SubhanAllah) and women to clap when needed during prayer.