How long have you had this male budgie?
It's good that you have rescued the male budgie and given the fact he was a lost stray, strict quarantine measures should have been followed before introducing him to your female. You should have quarantined the male on a different cage and room away from your female for at the very least a period of one month. This is done as preventative measure in order to safeguard your female and to avoid any potential illness carried by your rescued bird to be passed to your other budgie.
Before introducing any new pet bird, it's not advisable to just place the new bird into your other budgie's cage. By doing so without taking the proper time for introductions, the chances of them not getting along will be much higher.
Your older budgie will see this as an invasion of territory and will show hostility towards the newbie budgie. This is even more common when a new bird enters a female budgie's territory.
My advice for your specific case would be to separate your budgies into different cages. Place the cages close by for the first few weeks so they can see and communicate with each other. Allow your budgies closely supervised out of cage time together on a neutral territory and pay attention to their interactions.
Rearrange your female budgie's cage, do a total cage makeover and depending on how they get along you can then allow your budgies to share a cage or not. If they start to get along well they may even follow each other into one of the cages.
Take some time and give this rescue budgie a chance before thinking of rehoming him. He has already gone through a very rough time as a lost stray and needs good stability.
Best of luck with your budgies. Even if you find a good home for your male budgie and decide to get another budgie, be sure to follow the advice mentioned above or else you will run the risk of having the same issues happening again.