Is it permissible to combine the intention of fasting Rajab for the sake of Allah with the intention of solidarity with the prisoners?

Sometimes partnership in intention invalidates an act of worship, and sometimes it does not. Examples of when it does not invalidate include fasting for God and for health, or going on a hunger strike to achieve a benefit or avert harm. Al-Suyuti mentioned in "Al-Ashbah wa al-Naza'ir" that partnership in intention with something that is not an act of worship may or may not invalidate it. Examples of it not invalidating include intending ablution (wudu) or ritual bathing (ghusl (definition)) along with cooling oneself, or intending fasting along with dieting or medical treatment. The sounder opinion in these cases is that it remains valid. Ibn al-Humam, from the Hanafi school, alluded to this in "Fath al-Qadir," clarifying that dieting and medical treatment occur whether one intends them or not, so intending them is not considered partnership or a departure from sincerity. There is nothing authentic concerning the specific virtue of fasting in Rajab.