You can use bamtofastq from bedtools like this to get the pairs in separate files
bedtools bamtofastq -i http://ftp.ensembl.org/pub/release-79/data_files/mus_musculus/GRCm38/rnaseq/GRCm38.sanger.brain.1.bam -fq read1.fq -fq2 read2.fq
UPDATE:
The bam-file need to be sorted by read name for bamtofastq to pick them as read1/read2 one after other. Step-by-step
1 Download BAM (also see Note1)
$ wget http://ftp.ensembl.org/pub/release-79/data_files/mus_musculus/GRCm38/rnaseq/GRCm38.sanger.brain.1.bam
2 Check the integrity of dloaded bam-file
$ wget http://ftp.ensembl.org/pub/release-79/data_files/mus_musculus/GRCm38/rnaseq/md5sum.txt
$ grep GRCm38.sanger.brain.1.bam md5sum.txt > my.md5sum.txt
$ md5sum -c my.md5sum.txt
The last md5sum command should print OK, else re-download the file.
3 sort the bam ( -n = sort by read names; -@14 = 14 threads)
samtools sort -n -@14 GRCm38.sanger.brain.1.bam GRCm38.sanger.brain.1.sort
4 Run bam2fastq on sorted bam
bedtools bamtofastq -i GRCm38.sanger.brain.1.sort.bam -fq read1.fq -fq2 read2.fq
Notes
1 if you have axel installed, you can accelerate the download using multithreading. Axel, using 14 threads:
axel -a -n 14 http://ftp.ensembl.org/pub/release-79/data_files/mus_musculus/GRCm38/rnaseq/GRCm38.sanger.brain.1.bam
2
In addition, i think it will be more guarantee if we could download
the fastq file from some websites directly.
There is nothing to worry. The sequence-info and qual-scores are all there in standard well formated BAM-file, unless the reads are hard-clipped or the BAM-file is filtered.
PS: I searched but could not find the fastq file on web.