All you can do is make suggestions. Whether those suggestions are followed or not, at least you can feel good about doing so. Maybe some of those will make things easier on your partner, she just doesn't see it. I would make a list and hand a copy over to both of them.

I think if you really are coming with changes from a good place and someone on your team can't accept that, its their issue.

Things change all the time, re-evaluating processes is how you get better at things.

If your suggestions are valid you'll both benefit by bringing them up. Maybe your colleague doesn't want the change because she either likes the status quo or envisions more work. So maybe 'selling' her on the ideas in a way that she'll see things will be easier for her might be a good call.

Discuss your idea with your Team Leader, but tell your co-worker first about it that you're planning on doing this, but that you don't mean to step on her toes. Also at my work, any ideas are welcome, and my own bosses say "an idea is an idea, always good to share, it's like trying. You begin with doing without knowing the outcome." ;) You never know.. ;)

Your team leader asked for your opinion because he/she values it, or maybe your ideas are really good and TL wants to steal them to make him/her look good. In any event, your work flow should improve. You should sit with your partner and discuss the matter, even if you disagree on things. You write a brief report outlining both your suggestions, but make it clear that your partner disagrees on specific ones. Then sign it. Give a copy to you TL, and send a copy to his/her superior if you think that will not cause problems.

Don't be afraid to propose your new solution just because you think they won't understand it. I vote for giving it a try

If you can't move forward in some way at your job the job becomes a dead end and you should be thinking about leaving. You shouldn't consider the feelings of someone stuck in a rut when asked what you can improve. This could be a test to see if you can put aside personal feelings and make good decisions. You know, someone who can lead, someone who could move into a management position.

Tell them exactly what you just told us.

silentwriter180 & LilyOfTheValley users here have already responded precisely. Follow that being at your best - politely with tact.

Bests. 👍

Use process mapping to eliminate any waste in the process and propose updates.

Well people do get stuck in there ways. Maybe make your new plan and make up a case why it will benfit the team and how it will help you work better together so every one is happy ☺ while making a better contribution towards the company