What is Accepted from the Forgetful

Here is a blog post by IslamicSalvation, which can be found here:

باب ما يقبل من صلاة الساهي

Chapter on what is accepted from the prayer of the forgetful

محمد بن يحيى، عن أحمد بن محمد، عن الحسين بن سعيد، عن النضر بن سويد عن هشام بن سالم، عن محمد بن مسلم قال: قلت لابي عبدالله (عليه السلام): إن عمار الساباطي روى عنك رواية قال: وما هي؟ قلت: روى أن السنة فريضة، فقال: أين يذهب أين يذهب: ليس هكذا حدثته أنما قلت له: من صلى فأقبل على صلاته لم يحدث نفسه فيها أو لم يسه فيها أقبل الله عليه ما أقبل عليها، فربما رفع نصفها أو ربعها أو ثلثها أو خمسها وإنما أمرنا بالسنة ليكمل بها ما ذهب من المكتوبة - صحيح

Muhammad bin Yahya from Ahmad bin Muhammad from Husayn bin Said from Nadhr bin Suwayd from Hisham bin Salim from Muhammad bin Muslim who said : I said to Abi Abdillah (a.s) : Ammaar as-Sabitiy has narrated from you (on your authority) a narration, so He (a.s) said : and what is that (narration that he narrates)?  I said : He narrates that (you said) the ‘sunnah’ (recommended prayers) is a ‘faridha’ (obligation), So He (a.s) said: Where is he going, where is he going, that is not how I narrated it, rather I said to him : whoever prays and faces his prayer (turns to it) (concentrating fully) and does not corrupt himself in it nor forgets anything in it – Allah (s.w.t) accepts from him what He accepts of it, so it may happen that only a half, or a quarter, or a third, or a fifth of his prayer is raised (due to being the part meeting the aforementioned criterion from his prayer) and so we have been emphasised (lit. commanded) the ‘sunnah’ (recommended prayers) to complete what went awry from the obligatory prayers. (Sahih)

محمد بن يحيى، عن أحمد بن محمد، عن ابن أبي عمير، عن هشام بن سالم، عن محمد بن مسلم، عن أبي جعفر (عليه السلام) قال: إن العبد ليرفع له من صلاته نصفها أو ثلثها أو ربعها أو خمسها فما يرفع له إلا ما أقبل عليه بقلبه، وإنما أمرنا بالنافلة ليتم لهم بها ما نقصوا من الفريضة - صحيح

Muhammad bin Yahya from Ahmad bin Muhammad from Ibn Abi Umayr from Hisham bin Salim from Muhammad bin Muslim from Abi Ja’far (a.s) who said : Indeed for a  slave -  it is raised (accepted from him) of his prayer - a half of it, or a third of it, or a quarter of it, or a fifth of it, so nothing from the prayer is raised (and accepted) except for what he has faced of it with his whole heart (in attention), and we have therefore been emphasised (lit. commanded) the ‘nafila’ (recommended prayers) to complete what has been lost (remained with us unraised) from the obligatory prayers. (Sahih)  

علي بن إبراهيم، عن أبيه، ومحمد بن إسماعيل، عن الفضل بن شاذان جميعا، عن حماد بن عيسى، عن حريز، عن الفضيل بن يسار، عن أبي جعفر وأبي عبدالله (عليه السلام) أنهما قالا: إنما لك من صلاتك ما أقبلت عليه منها فإن أوهمها كلها أو غفل عن أدائها لفت فضرب بها وجه صاحبها - حسن كالصحيح

Ali bin Ibrahim from his father (Ibrahim bin Hashim) AND Muhammad bin Ismail from Fadhl bin Shadhan all togethor from Hammad bin Isa from Hariz (bin Abdillah) from Fudhayl bin Yasar from Abi Ja’far AND Abi Abdillah (a.s) that they said : Indeed it is for you from your prayer what you gave attention to, so if one is inattentive throughout or careless in its performance (delaying or hastening it), it (the prayer is taken) crumpled up and thrown back at the face of the one who offered it. (Hasan like Sahih)

علي بن إبراهيم، عن أبيه، عن عبدالله بن المغيرة قال: في كتاب حريز أنه قال: إني نسيت أني في صلاة فريضة حتى ركعت وأنا أنويها تطوعا قال: فقال هي التي قمت فيها إن كنت قمت وأنت تنوي فريضة ثم دخلك الشك فأنت في الفريضة و إن كنت دخلت في نافلة فنويتها فريضة فأنت في النافلة وإن كنت دخلت في فريضة ثم ذكرت نافلة كانت عليك فامض في الفريضة - حسن

Ali bin Ibrahim from his father (Ibrahim bin Hashim) from Abdallah bin Mughira who said : in the book of Hariz (bin Abdillah) (it is written) that he said : I forgot that I was in a Faridha (obligatory) prayer until I went into Rukuu and I (may have) made a Niyyah of it being a Nafila (recommended) prayer, so He (a.s) said : It is what you stood up for (originally intended), if you stood up to pray and you intend the Faridha then doubt enters your mind (while praying about you Niyyah during Takbir) then you are in the Faridha and if you entered into (for) the Nafila and (may) have made Niyyah of the Faridha (during takbir) then you are in the Nafila and if you entered into (for) the Faridha and then (while praying) remembered that you hadmade Niyyah (during takbir) to pray the Nafila then remain in the Faridha (continue with it to finish it first). (Hasan due to Ibrahim bin Hashim)